Patrick Valageas

French National Centre for Scientific Research, Lutetia Parisorum, Île-de-France, France

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Publications (84)344.07 Total impact

  • Source
    Dipak Munshi · Geraint Pratten · Patrick Valageas · Peter Coles · Philippe Brax
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    ABSTRACT: We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier-Bessel (sFB) basis. We use a fully non-linear description of the real-space matter power-spectrum and include the lowest-order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different modified gravity scenarios, namely the generalised Dilaton scalar-tensor theories and the $f({R})$ models in the large curvature regime. We compute the 3D power spectrum ${\cal C}^s_{\ell}(k_1,k_2)$ for various such MG theories with and without redshift space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function $\varphi(r)\propto \exp(-{r^2 / r^2_0})$, $r_0 = 150 \, h^{-1} \, {\textrm{Mpc}}$, and number density of galaxies $\bar {\textrm{N}} =10^{-4}\;{\textrm{Mpc}}^{-3}$, we use a $\chi^2$ analysis, and find that the lower-order $(\ell \leq 25)$ multipoles of ${\cal C}^s_\ell(k,k')$ (with radial modes restricted to $k < 0.2 \, h \,{\textrm{Mpc}}^{-1}$) can constraint the parameter $f_{R_0}$ at a level of $2\times 10^{-5} (3\times 10^{-5})$ with $3 \sigma$ confidence for $n=1(2)$. Combining constraints from higher $\ell > 25$ modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with solar system tests. However this will require an accurate modelling of non-linear redshift space distortions. Using a tomographic $\beta(a)$-$m(a)$ parameterization we also derive constraints on specific parameters describing the Dilaton models of modified gravity.
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    ABSTRACT: We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {\it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General-Relativity + $\Lambda$CDM scenario occurs at $k\sim1 h \mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $\xi_{\pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ $\{ |f_{R_0}|=10^{-4}, n=1\}$ model with more than 99.9% confidence interval (CI) when assuming a $\Lambda$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the $\{ |f_{R_0}|=10^{-4}, n=2\}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.
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    Philippe Brax · Luca Alberto Rizzo · Patrick Valageas
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    ABSTRACT: We investigate the effects of a K-mouflage modification of gravity on the dynamics of clusters of galaxies. We extend the description of K-mouflage to situations where the scalar field responsible for the modification of gravity is coupled to a perfect fluid with pressure. We describe the coupled system at both the background cosmology and cosmological perturbations levels, focusing on cases where the pressure emanates from small-scale nonlinear physics. We derive these properties in both the Einstein and Jordan frames, as these two frames already differ by a few percents at the background level for K-mouflage scenarios, and next compute cluster properties in the Jordan frame that is better suited to these observations. Galaxy clusters are not screened by the K-mouflage mechanism and therefore feel the modification of gravity in a maximal way. This implies that the halo mass function deviates from $\Lambda$-CDM by a factor of order one for masses $M\gtrsim 10^{14} \ h^{-1} M_\odot$. We then consider the hydrostatic equilibrium of gases embedded in galaxy clusters and the consequences of K-mouflage on the X-ray cluster luminosity, the gas temperature and the Sunyaev-Zel'dovich effect. We find that the cluster temperature function, and more generally number counts, are largely affected by K-mouflage, mainly due to the increased cluster abundance in these models. Other scaling relations such as the mass-temperature and the temperature-luminosity relations are only modified at the percent level due to the constraints on K-mouflage from local Solar System tests.
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    ABSTRACT: We show that Solar System tests can place very strong constraints on K-mouflage models of gravity, which are coupled scalar field models with nontrivial kinetic terms that screen the fifth force in regions of large gravitational acceleration. In particular, the bounds on the anomalous perihelion of the Moon imposes stringent restrictions on the K-mouflage Lagrangian density, which can be met when the contributions of higher order operators in the static regime are sufficiently small. The bound on the rate of change of the gravitational strength in the Solar System constrains the coupling strength $\beta$ to be smaller than $0.1$. These two bounds impose tighter constraints than the results from the Cassini satellite and Big Bang Nucleosynthesis. Despite the Solar System restrictions, we show that it is possible to construct viable models with interesting cosmological predictions. In particular, relative to $\Lambda$-CDM, such models predict percent level deviations for the clustering of matter and the number density of dark matter haloes. This makes these models predictive and testable by forthcoming observational missions.
    Physical Review D 04/2015; 91(12). DOI:10.1103/PhysRevD.91.123522 · 4.86 Impact Factor
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    Takahiro Nishimichi · Patrick Valageas
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    ABSTRACT: We present the redshift-space generalization of the equal-time angular-averaged consistency relations between $(\ell+n)$- and $n$-point polyspectra of the cosmological matter density field. Focusing on the case of $\ell=1$ large-scale mode and $n$ small-scale modes, we use an approximate symmetry of the gravitational dynamics to derive explicit expressions that hold beyond the perturbative regime, including both the large-scale Kaiser effect and the small-scale fingers-of-god effects. We explicitly check these relations, both perturbatively, for the lowest-order version that applies to the bispectrum, and nonperturbatively, for all orders but for the one-dimensional dynamics. Using a large ensemble of $N$-body simulations, we find that our squeezed bispectrum relation is valid to better than $20\%$ up to $1h$Mpc$^{-1}$, for both the monopole and quadrupole at $z=0.35$, in a $\Lambda$CDM cosmology. Additional simulations done for the Einstein-de Sitter background suggest that these discrepancies mainly come from the breakdown of the approximate symmetry of the gravitational dynamics. For practical applications, we introduce a simple ansatz to estimate the new derivative terms in the relation using only observables. Although the relation holds worse after using this ansatz, we can still recover it within $20\%$ up to $1h$Mpc$^{-1}$, at $z=0.35$ for the monopole. On larger scales, $k = 0.2 h\mathrm{Mpc}^{-1}$, it still holds within the statistical accuracy of idealized simulations of volume $\sim8h^{-3}\mathrm{Gpc}^3$ without shot-noise error.
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    ABSTRACT: We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, massless and massive neutrinos, in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the CMB, lensing potential and matter power spectra are affected by the fifth force, and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology, or those who are interested in the cosmological behaviour of the K-mouflage model.
    Physical Review D 11/2014; 91(6). DOI:10.1103/PhysRevD.91.063528 · 4.86 Impact Factor
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    ABSTRACT: This paper presents 52 X-ray bright galaxy clusters selected within the 11 deg2 XMM-LSS survey. 51 of them have spectroscopic redshifts (0.05 < z < 1.06), one is identified at zphot = 1.9, and all together make the high-purity ‘Class 1’ (C1) cluster sample of the XMM-LSS, the highest density sample of X-ray-selected clusters with a monitored selection function. Their X-ray fluxes, averaged gas temperatures (median TX = 2 keV), luminosities (median LX, 500 = 5 × 1043 erg s−1) and total mass estimates (median 5 × 1013 h−1 M⊙) are measured, adapting to the specific signal-to-noise regime of XMM-LSS observations. Particular care is taken in deriving the sample selection function by means of realistic simulations reproducing the main characteristics of XMM observations. The redshift distribution of clusters shows a deficit of sources when compared to the cosmological expectations, regardless of whether Wilkinson Microwave Anisotropy Probe-9 or Planck-2013 cosmic microwave background parameters are assumed. This lack of sources is particularly noticeable at 0.4 ≲ z ≲ 0.9. However, after quantifying uncertainties due to small number statistics and sample variance, we are not able to put firm (i.e. >3σ) constraints on the presence of a large void in the cluster distribution. We work out alternative hypotheses and demonstrate that a negative redshift evolution in the normalization of the LX-TX relation (with respect to a self-similar evolution) is a plausible explanation for the observed deficit. We confirm this evolutionary trend by directly studying how C1 clusters populate the LX-TX-z space, properly accounting for selection biases. We also point out that a systematically evolving, unresolved, central component in clusters and groups (AGN contamination or cool core) can impact the classification as extended sources and be partly responsible for the observed redshift distribution. We provide in a table the catalogue of 52 clusters together with their measured properties.
    Monthly Notices of the Royal Astronomical Society 08/2014; 444(3). DOI:10.1093/mnras/stu1625 · 5.23 Impact Factor
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    Philippe Brax · Patrick Valageas
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    ABSTRACT: We investigate the small-scale static configurations of K-mouflage models defined by a general function $K(\chi)$ of the kinetic terms. The fifth force is screened by the nonlinear K-mouflage mechanism if $K'(\chi)$ grows sufficiently fast for large negative $\chi$. In the general non-spherically symmetric case, the fifth force is not aligned with the Newtonian force. For spherically symmetric static matter density profiles, the results depend on the potential function $W_{-}(y) = y K'(-y^2/2)$, which must be monotonically increasing to $+\infty$ for $y \geq 0$ to guarantee the existence of a single solution throughout space for any matter density profile. Starting from vanishing initial conditions or from nearby profiles, we numerically check that the scalar field converges to the static solution. If $W_{-}$ is bounded, for high-density objects there are no static solutions throughout space, but one can still define a static solution restricted to large radii. Our dynamical study shows that the scalar field relaxes to this static solution at large radii, whereas spatial gradients keep growing with time at smaller radii. If $W_{-}$ is not bounded but non-monotonic, there are an infinite number of discontinuous static solutions but these are not physical and those models are not theoretically sound. Such K-mouflage scenarios provide an example of theories that can appear viable at the cosmological level, for the cosmological background and perturbative analysis, while being meaningless at a nonlinear level for small scale configurations. This shows the importance of small-scale nonlinear analysis of screening models.
    Physical Review D 08/2014; 90(12). DOI:10.1103/PhysRevD.90.123521 · 4.86 Impact Factor
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    Julien Bel · Philippe Brax · Christian Marinoni · Patrick Valageas
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    ABSTRACT: The clustering ratio $\eta$, a large-scale structure observable originally devised to constrain the shape of the power spectrum of matter density fluctuations, is shown to provide a sensitive and model independent probe of the nature of gravity in the cosmological regime. We apply this analysis to $F(R)$ theories of gravity using the luminous red galaxy sample extracted from the Sloan Digital Sky Survey. We find that the absolute amplitude of deviations from GR, $f_{R_0 }$, is constrained to be smaller than $3 \times 10^{-6}$ at the 1$\sigma$ confidence level. This bound, improving by an order of magnitude on current constraints, makes cosmological probes of gravity competitive with Solar system tests.
    Physical Review D 06/2014; 91(10). DOI:10.1103/PhysRevD.91.103503 · 4.86 Impact Factor
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    Philippe Brax · Patrick Valageas
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    ABSTRACT: We study structure formation in K-mouflage cosmology whose main feature is the absence of screening effect on quasi-linear scales. We show that the growth of structure at the linear level is both affected by a new time dependent Newton constant and a friction term which depend on the background evolution. These combine with the modified background evolution to change the growth rate by up to ten percent since $z\sim 2$. At the one loop level, we find that the non-linearities of the K-mouflage models are mostly due to the matter dynamics and that the scalar perturbations can be treated at tree level. We also study the spherical collapse in K-mouflage models and show that the critical density contrast deviates from its $\Lambda$-CDM value and that, as a result, the halo mass function is modified for large masses by an order one factor. Finally we consider the deviation of the matter spectrum from $\Lambda$-CDM on non-linear scales where a halo model is utilised. We find that the discrepancy peaks around $1\ h{\rm Mpc}^{-1}$ with a relative difference which can reach fifty percent. Importantly, these features are still true at larger redshifts, contrary to models of the chameleon-$f(R)$ and Galileon types.
    Physical Review D 03/2014; 90(2). DOI:10.1103/PhysRevD.90.023508 · 4.86 Impact Factor
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    Philippe Brax · Patrick Valageas
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    ABSTRACT: We study the cosmology of K-mouflage theories at the background level. We show that the effects of the scalar field are suppressed at high matter density in the early Universe and only play a role in the late time Universe where the deviations of the Hubble rate from its $\Lambda$-CDM counterpart can be of order five percent for redshifts $1 \lesssim z \lesssim 5$. Similarly, we find that the equation of state can cross the phantom divide in the recent past and even diverge when the effective scalar energy density goes negative and subdominant compared to matter, preserving the positivity of the squared Hubble rate. These features are present in models for which Big Bang Nucleosynthesis is not affected. We analyse the fate of K-mouflage when the nonlinear kinetic terms give rise to ghosts, particle excitations with negative energy. In this case, we find that the K-mouflage theories can only be considered as an effective description of the Universe at low energy below $1$ keV. In the safe ghost-free models, we find that the equation of state always diverges in the past and changes significantly by a few percent since $z\lesssim 1$.
    Physical Review D 03/2014; 90(2). DOI:10.1103/PhysRevD.90.023507 · 4.86 Impact Factor
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    Takahiro Nishimichi · Patrick Valageas
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    ABSTRACT: We explicitly test the equal-time consistency relation between the angular-averaged bispectrum and the power spectrum of the matter density field, employing a large suite of cosmological $N$-body simulations. This is the lowest-order version of the relations between $(\ell+n)-$point and $n-$point polyspectra, where one averages over the angles of $\ell$ soft modes. This relation depends on two wave numbers, $k'$ in the soft domain and $k$ in the hard domain. We show that it holds up to a good accuracy, when $k'/k\ll 1$ and $k'$ is in the linear regime, while the hard mode $k$ goes from linear ($0.1\,h\,\mathrm{Mpc}^{-1}$) to nonlinear ($1.0\,h\,\mathrm{Mpc}^{-1}$) scales. On scales $k\lesssim 0.4\,h\,\mathrm{Mpc}^{-1}$, we confirm the relation within a $\sim 5\%$ accuracy, even though the bispectrum can already deviate from leading-order perturbation theory by more than $30\%$. We further show that the relation extends up to nonlinear scales, $k \sim 1.0\,h\,\mathrm{Mpc}^{-1}$, within an accuracy of $\sim 10\%$.
    Physical Review D 02/2014; 90(2). DOI:10.1103/PhysRevD.90.023546 · 4.86 Impact Factor
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    Patrick Valageas
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    ABSTRACT: Aims: We estimate the amplitude of the source-lens clustering bias and of the intrinsic-alignment bias of weak-lensing estimators of the two-point and three-point convergence and cosmic-shear correlation functions. Methods: We use a linear galaxy bias model for the galaxy-density correlations, as well as a linear intrinsic-alignment model. For the three-point and four-point density correlations, we use analytical or semi-analytical models, based on a hierarchical ansatz or a combination of one-loop perturbation theory with a halo model. Results: For two-point statistics, we find that the source-lens clustering bias is typically several orders of magnitude below the weak-lensing signal, except when we correlate a very low-redshift galaxy (z2 ≲ 0.05) with a higher redshift galaxy (z1 ≳ 0.5), where it can reach 10% of the signal for the shear. For three-point statistics, the source-lens clustering bias is typically on the order of 10% of the signal, as soon as the three galaxy source redshifts are not identical. The intrinsic-alignment bias is typically about 10% of the signal for both two-point and three-point statistics. Thus, both source-lens clustering bias and intrinsic-alignment bias must be taken into account for three-point estimators aiming at a better than 10% accuracy. Appendices are available in electronic form at http://www.aanda.org
    Astronomy and Astrophysics 01/2014; 561:53-. DOI:10.1051/0004-6361/201322146 · 4.48 Impact Factor
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    Patrick Valageas
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    ABSTRACT: The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular averaged consistency relations for the matter density correlations. This allows one to write the $(\ell+n)$ density correlation, with $\ell$ large-scale linear wave numbers that are integrated over angles, and $n$ fixed small-scale nonlinear wave numbers, in terms of the small-scale $n$-point density correlation and $\ell$ prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help designing analytical models of gravitational clustering.
    Physical Review D 11/2013; 89(12). DOI:10.1103/PhysRevD.89.123522 · 4.86 Impact Factor
  • Patrick Valageas
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    ABSTRACT: We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how the $(\ell+n)$-density correlation factors in terms of the $n$-point correlation and $\ell$ linear power spectrum factors, in the limit where the $\ell$ soft wave numbers become linear and much smaller than the $n$ other wave numbers. We show how these relations extend to multi-fluid cases. These consistency relations are not equivalent to the Galilean invariance nor to the equivalence principle, as both can be violated and the relations remain valid. We describe how these relations are due to a weak form of scale separation and that a detection of their violation would indicate non-Gaussian initial conditions or a modification of gravity that does not converge to General Relativity on large scales.
    Physical Review D 11/2013; 89(8). DOI:10.1103/PhysRevD.89.083534 · 4.86 Impact Factor
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    Patrick Valageas
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    ABSTRACT: We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo model, we study the convergence rate of several perturbative expansion schemes and the impact of nonperturbative effects, as well as the sensitivity to phenomenological halo parameters. We check that the simple reorganization of the standard perturbative expansion, with a Gaussian damping prefactor, provides a well-ordered convergence and a finite correlation function that yields a percent accuracy at the BAO peak (as soon as one goes to second order). Lagrangian-space expansions are somewhat more efficient, when truncated at low orders, but may diverge at high orders. We find that whereas the uncertainty on the halo-profile mass-concentration relation is not a strong limitation, the uncertainty on the halo mass function can severely limit the accuracy of theoretical predictions for $P(k)$. The real-space correlation function provides a better separation between perturbative and nonperturbative effects, which are restricted to $x \lesssim 10 h^{-1}$Mpc at all redshifts.
    Physical Review D 08/2013; 88(8). DOI:10.1103/PhysRevD.88.083524 · 4.86 Impact Factor
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    Philippe Brax · Patrick Valageas
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    ABSTRACT: We study the effects of screened modified gravity of the $f(R)$, dilaton and symmetron types on structure formation, from the quasi-linear to the non-linear regime, using semi-analytical methods. For such models, where the range of the new scalar field is typically within the Mpc range and below in the cosmological context, non-linear techniques are required to understand the deviations of the power spectrum of the matter density contrast compared to the $\Lambda$-CDM template. This is nowadays commonly tackled using extensive N-body simulations. Here we present new results combining exact perturbation theory at the one loop level (and a partial resummation of the perturbative series) with a halo model. The former allows one to extend the linear perturbative analysis up to $k\lesssim 0.15{\rm h Mpc}^{-1}$ at the perturbative level while the latter leads to a reasonable, up to a few percent, agreement with numerical simulations for $k\lesssim 3{\rm h Mpc}^{-1}$ for large curvature $f(R)$ models, and $k\lesssim 1{\rm h Mpc}^{-1}$ for dilatons and symmetrons, at $z=0$. We also discuss how the behaviors of the perturbative expansions and of the spherical collapse differ for $f(R)$, dilaton, and symmetron models.
    Physical review D: Particles and fields 05/2013; 88(2). DOI:10.1103/PhysRevD.88.023527 · 4.86 Impact Factor
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    Patrick Valageas · Takahiro Nishimichi · Atsushi Taruya
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    ABSTRACT: We present a new approach to computing the matter density power spectrum, from large linear scales to small highly nonlinear scales. Instead of explicitly computing a partial series of high-order diagrams, as in perturbative resummation schemes, we embed the standard perturbation theory within a realistic nonlinear Lagrangian-space ansatz. We also point out that an "adhesion-like" regularization of the shell-crossing regime is more realistic than a "Zel'dovich-like" behavior, where particles freely escape to infinity. This provides a "cosmic web" power spectrum with good small-scale properties that provide a good matching with a halo model on mildly nonlinear scales. We obtain a good agreement with numerical simulations on large scales, better than 3% for $k\leq 1 h$Mpc$^{-1}$, and on small scales, better than 10% for $k \leq 10 h$Mpc$^{-1}$, at $z \geq 0.35$, which improves over previous methods.
    Physical review D: Particles and fields 02/2013; 87(8). DOI:10.1103/PhysRevD.87.083522 · 4.86 Impact Factor
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    Patrick Valageas
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    ABSTRACT: We investigate whether the late-time (at $z\leq 100$) velocity dispersion expected in Warm Dark Matter scenarios could have some effect on the cosmic web (i.e., outside of virialized halos). We consider effective hydrodynamical equations, with a pressurelike term that agrees at the linear level with the analysis of the Vlasov equation. Then, using analytical methods, based on perturbative expansions and the spherical dynamics, we investigate the impact of this term for a 1 keV dark matter particle. We find that the late-time velocity dispersion has a negligible effect on the power spectrum on perturbative scales and on the halo mass function. However, it has a significant impact on the probability distribution function of the density contrast at $z \sim 3$ on scales smaller than $0.1 h^{-1}$Mpc, which correspond to Lyman-$\alpha$ clouds. Finally, we note that numerical simulations should start at $z_i\geq 100$ rather than $z_i \leq 50$ to avoid underestimating gravitational clustering at low redshifts.
    Physical review D: Particles and fields 06/2012; 86(12). DOI:10.1103/PhysRevD.86.123501 · 4.86 Impact Factor
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    Philippe Brax · Patrick Valageas
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    ABSTRACT: We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the $f(R)$ models and more generally to screened modified gravity models. We investigate the linear and weakly nonlinear regimes using the "standard" perturbative approach and a resummation technique, while we use the spherical dynamics to go beyond low-order results. This allows us to estimate the matter density power spectrum and bispectrum from linear to highly nonlinear scales, the full probability distribution of the density contrast on weakly nonlinear scales, and the halo mass function. We analyse the impact of modifications of gravity on these quantities for a few realistic models. In particular, we find that the standard one-loop perturbative approach is not sufficiently accurate to probe these effects on the power spectrum and it is necessary to use resummation methods even on weakly nonlinear scales which provide the best observational window for modified gravity as relative deviations from General Relativity do not grow significantly on smaller scales where theoretical predictions become increasingly difficult.
    Physical review D: Particles and fields 05/2012; 86(6). DOI:10.1103/PhysRevD.86.063512 · 4.86 Impact Factor

Publication Stats

930 Citations
344.07 Total Impact Points

Institutions

  • 2011–2014
    • French National Centre for Scientific Research
      • Institut d'astrophysique spatiale (IAS)
      Lutetia Parisorum, Île-de-France, France
  • 2012
    • Institute of Geophysics, China Earthquake Administration
      Peping, Beijing, China
  • 2008–2010
    • Cea Leti
      Grenoble, Rhône-Alpes, France
  • 1999
    • University of California, Berkeley
      Berkeley, California, United States