arXiv:1002.4096v2 [hep-ph] 25 Feb 2010
LHC and ILC Data and the Early Universe Properties
A. Arbey(1), F. Mahmoudi(2)
(1) Universit´ e de Lyon, France; Universit´ e Lyon 1, F–69622; CRAL, Observatoire de Lyon,
F–69561 Saint-Genis-Laval; CNRS, UMR 5574; ENS de Lyon, France.
(2) Clermont Universit´ e, Universit´ e Blaise Pascal, CNRS/IN2P3,
LPC, BP 10448, 63000 Clermont-Ferrand, France.
Summary. — With the start-up of the LHC, we can hope to find evidences for
new physics beyond the Standard Model, and particle candidates for dark matter.
Determining the parameters of the full underlying theory will be a long process
requiring the combination of LHC and ILC data, flavor physics constraints, and
cosmological observations. However, the Very Early Universe properties, from which
the relic particles originate, are poorly known, and the relic density calculation can
be easily falsified by hidden processes. We consider supersymmetry and show that
determining the underlying particle physics parameters will help understanding the
Very Early Universe properties.
PACS 11.30.Pb – Supersymmetry.
PACS 95.35.+d – Dark matter.
PACS 98.80.Cq – Particle-theory and field-theory models of the early Universe.
1. – Introduction
The present and future high energy colliders will hopefully allow the discovery of
new particles. Many new physics models beyond the Standard Model propose particle
candidates for dark matter, within the reach of the LHC and ILC. Should a stable, neutral
and weakly interacting new particle be found, it would be a candidate for dark matter.
Through particle physics computation of annihilation and co-annihiliation diagrams, it
is possible to compute the dark matter relic density . This relic density is then often
compared to the dark matter density deduced from cosmological observations in order to
constrain new physics parameters. If the computed relic density is compatible with the
cosmologically inferred dark matter density, the cosmological model will be reinforced by
this new particle discovery. However, in case of disagreements, two possible paths can
open: either the new physics particle model is not correctly designed, or the cosmological
model is missing ingredients, such as quintessence  or reheating . In [4, 5], we showed
that such dark components can modify the computed relic density by several orders of
magnitudes, and we introduced parametrizations to characterize the Very Early Universe
A. ARBEY, F. MAHMOUDI
properties. Using this kind of parametrizations, and combining with particle physics data,
it will therefore be possible to determine the Very Early Universe properties beyond the
standard cosmological scenario. In the following we will consider Supersymmetry (SUSY)
as an example and discuss the use of relic density to constrain cosmological properties.
2. – Relic density calculation
The density number of supersymmetric particles is determined by the Boltzmann
equation and takes the form:
dt= −3Hn − ?σv?(n2− n2
where n is the number density of supersymmetric particles, ?σv? is the thermally averaged
annihilation cross-section, H is the Hubble expansion rate and neqis the supersymmet-
ric particle equilibrium number density. The expansion rate H is determined by the
(ρrad+ ρD) . (2)
ρradis the radiation energy density, which is considered to be dominant before BBN in
the standard cosmological model. ρDis introduced in Eq. (2) to parametrize the expan-
sion rate modification  and can be interpreted either as an additional energy density
modifying the expansion (e.g. quintessence), or as an effective energy density which can
account for other phenomena affecting the expansion rate (e.g. extra-dimensions).
The entropy evolution can also be altered beyond the standard cosmological model.
In presence of entropy fluctuations we give the entropy evolution equation:
dt= −3Hs + ΣD, (3)
where s is the total entropy density. ΣDin the above equation parametrizes effective en-
tropy fluctuations due to unknown properties of the Early Universe, and is temperature-
The parameters ρD and ΣD can be regarded as independent. Entropy and energy
alterations are considered here as effective effects, and can be generated by curvature,
phase transitions, extra-dimensions, or other phenomena in the Early Universe. In a
specific physical scenario, these parameters can be related, as for example in reheating
The radiation energy and entropy densities can be written as usual:
We split the total entropy density into two parts: radiation entropy density and effective
dark entropy density, s ≡ srad+sD. Using Eq. (3) the relation between sDand ΣDcan
then be derived:
?1 + ˜ ρDT2
LHC AND ILC DATA AND THE EARLY UNIVERSE PROPERTIES
Following the standard relic density calculation method , Y ≡ n/s is introduced, and
Eq. (1) yields
where x = mlsp/T, mlspis the mass of the lightest supersymmetric relic particle, and
1 + ˜ sD
√1 + ˜ ρD
45T3?2(1 + ˜ sD)2
(1 + ˜ sD)
with i running over all supersymmetric particles of mass mi and with gi degrees of
freedom. Integrating Eq. (7), the relic density can then be calculated using:
= 2.755× 108Y0mlsp/GeV ,(10)
where the subscript 0 refers to the present value of the parameters. In the limit where
ρD= sD= ΣD= 0, standard relations are retrieved. Using Eqs. (1-10) the relic density
in presence of a modified expansion rate and of entropy fluctuations can be computed
provided ρD and sD are specified. For ρD we follow the parametrization introduced in
where TBBNis the BBN temperature. Different values of nρleads to different behaviors
of the effective density. For example, nρ= 4 corresponds to a radiation behavior, nρ= 6
to a quintessence behavior, and nρ> 6 to the behavior of a decaying scalar field. κρis
the ratio of the effective energy density to the radiation energy density at BBN time and
can be negative. The role of ρDis to increase the expansion rate for ρD> 0, leading to
an early decoupling and a higher relic density, or to decrease it for ρD< 0, leading to a
late decoupling and to a smaller relic density. To model the entropy perturbations, we
follow the parametrization introduced in Ref. :
This parametrization finds its roots in the first law of thermodynamics, where energy
and entropy are directly related and therefore the entropy parametrization can be similar
to the energy parametrization. As for the energy density, different values of nslead to
A. ARBEY, F. MAHMOUDI
different behaviors of the entropy density: ns= 3 corresponds to a radiation behavior,
ns = 4 appears in dark energy models, ns ∼ 1 in reheating models, and other values
can be generated by curvature, scalar fields or extra-dimension effects. κsis the ratio of
the effective entropy density to the radiation entropy density at BBN time and can be
negative. The role of sDis to increase the temperature at which the radiation dominates
for sD> 0, leading to a decreased relic density, or to decrease this temperature for sD< 0,
increasing the relic density. Constraints on the cosmological entropy in reheating models
have been derived in .
3. – SUSY constraints
We now consider the effects of the parametrizations described in the previous section
on the supersymmetric constraints. Using the latest WMAP data  with an additional
10% theoretical uncertainty on the relic density calculation, we give the following favored
interval at 95% C.L.:
0.088 < ΩDMh2< 0.123 . (13)
The older dark matter interval is also considered:
0.1 < ΩDMh2< 0.3 . (14)
One million random SUSY points in the NUHM parameter plane (µ,mA) with m0 =
m1/2= 1 TeV, A0 = 0, tanβ = 40 are generated using SOFTSUSY v2.0.18 , and
for each point we compute flavor physics observables, direct limits and the relic density
with SuperIso Relic v2.7 [9, 10]. In Fig. 1, the effects of the cosmological models on
the relic density constraints are demonstrated. The first plot is given as a reference for
the standard cosmological model, showing the tiny strips corresponding to the regions
favored by the relic density constraint. In the second plot, generated in a Universe with
an additional energy density with κρ= 10−4and nρ= 6, the relic density favored strips
are reduced, since the calculated relic densities are decreased in comparison to the relic
densities computed in the standard scenario. The next plots demonstrate the influence
of an additional entropy density compatible with BBN constraints. The favored strips
are this time enlarged and moved towards the outside of the plot. This effect is due to a
decrease in the relic density. These figures show that a modification in the cosmological
scenario can completely modify the calculated relic density and lead to different shapes
of the favored parameter regions.
4. – Inverse Problem
The determination of the supersymmetric parameters using particle physics observ-
ables can on the other hand give access to global properties of the relic particle decou-
pling period . Let us consider the NUHM example point (m0 = m1/2= 1 TeV,
mA= µ = 500 GeV, A0= 0, tanβ = 40), which gives a relic density of Ωh2≈ 0.11 in
the cosmological standard model, compatible with WMAP results. The effects due to
the presence of effective energy or entropy in the Early Universe are presented in Fig.
2: the first plot shows the influence of an additional effective density on the computed
relic density. We note that when κρand nρincrease, the relic density increases up to a
factor of 105. The second plot illustrates the effect of an additional entropy density, in
LHC AND ILC DATA AND THE EARLY UNIVERSE PROPERTIES
Fig. 1. – Constraints on the NUHM parameter plane (µ,mA), in the standard cosmological model
(top left), in presence of a tiny energy overdensity with κρ = 10−4and nρ = 6 (top right), and
of an entropy overdensity with κs = 10−5and ns = 5 (bottom left), with κs = 10−4and ns = 5
(bottom right). The red points are excluded by the isospin asymmetry of B → K∗γ, the gray
points by direct collider limits, the yellow zones involve tachyonic particles, and the dark and
light blue strips are favored by the dark matter constraints of Eqs. (13) and (14) respectively.
absence of additional energy density. Here when κsand nsincrease, the relic density is
strongly decreased down to a factor of 10−14. The dark lines delimit the zones which are
compatible with WMAP data. The determination of the NUHM parameters provides
therefore interesting constraints on the cosmological properties of the Early Universe.
It is important to point out that all the cosmological scenarios previously described
are equivalent from the point of view of the cosmological observations: there is no way
to distinguish between them with the current cosmological data.
5. – Conclusion
We discussed the use of the LHC and ILC data, as well as flavor physics constraints,
together with the dark matter relic density evaluation, to explore the properties of the
Very Early Universe. In particular, we provided parametrizations of the entropy content
and the expansion rate for this purpose. We have shown that a disagreement between the
computed relic density and the observed dark matter density may be a sign of deviation
A. ARBEY, F. MAHMOUDI
Fig. 2. – Influence of the presence of an effective energy density with nρ = 6 (left), and an
effective entropy with ns = 5 (right). The colors correspond to different values of Ωh2. The
black lines delimit the regions favored by WMAP. The favored zones are the lower left corners.
from the standard cosmological model. Should high energy colliders discover candidates
for dark matter, such studies of the Early Universe properties will become possible.
 Goldberg H., Phys. Rev. Lett., 50 (1983) 1419; Krauss L.M., Nucl. Phys. B, 227
(1983) 556; Srednicki M., Watkins R. and Olive K.A., Nucl. Phys. B, 310 (1988) 693;
Gondolo P. and Gelmini G., Nucl. Phys. B, 360 (1991) 145; Edsj¨ o J. and Gondolo P.,
Phys. Rev. D, 56 (1997) 1879; Battaglia M., New J. Phys., 11 (2009) 105025.
 Kamionkowski M. and Turner M.S., Phys. Rev. D, 42 (1990) 3310; Rosati F., Phys.
Lett. B, 570 (2003) 5; Comelli D., Pietroni M. and Riotto A., Phys. Lett. B, 571
(2003) 115; Salati P., Phys. Lett. B, 571 (2003) 121; Profumo S. and Ullio P., JCAP,
0311 (2003) 006; Catena R. et al., Phys. Rev. D, 70 (2004) 063519; Pallis C., JCAP,
0510 (2005) 015; Chung D.J.H. et al., JHEP, 0710 (2007) 016.
 Scherrer R.J. and Turner M.S., Phys. Rev. D, 31 (1985) 681; Moroi T. and
Randall L., Nucl. Phys. B, 570 (2000) 455; Giudice G.F., Kolb E.W. and Riotto A.,
Phys. Rev. D, 64 (2001) 023508; Fornengo N., Riotto A., and Scopel S., Phys. Rev. D,
67 (2003) 023514; Pallis C., Astrop. Phys., 21 (2004) 689; Gelmini G. and Gondolo P.,
Phys. Rev. D, 74 (2006) 023510; Gelmini G. et al., Phys. Rev. D, 74 (2006) 083514;
Drees M., Iminniyaz H. and Kakizaki M., Phys. Rev. D, 76 (2007) 103524.
 Arbey A. and Mahmoudi F., Phys. Lett. B, 669 (2008) 46.
 Arbey A. and Mahmoudi F., arXiv:0906.0368 [hep-ph].
 Kawasaki M., Kohri K. and Sugiyama N., Phys. Rev. Lett., 82 (1999) 4168; Phys.
Rev. D, 62 (2000) 023506; Hannestad S., Phys. Rev. D, 70 (2004) 043506; Ichikawa K.,
Kawasaki M. and Takahashi F., Phys. Rev. D, 72 (2005) 043522.
 Dunkley J. et al., Astrophys. J. Suppl., 180 (2009) 306.
 Allanach B.C., Comput. Phys. Commun., 143 (2002) 35.
 Mahmoudi F., Comput. Phys. Commun., 178 (2008) 745; Mahmoudi F., Comput. Phys.
Commun., 180 (2009) 1579, http://superiso.in2p3.fr.
 Arbey A. and Mahmoudi F., arXiv:0906.0369, http://superiso.in2p3.fr/relic.
 Allanach B.C. et al., JHEP, 0412 (2004) 20; Baltz E.A.et al., Phys. Rev. D, 74 (2006)
103521; Roszkowski L., Ruiz de Austri R. and Trotta R., arXiv:0907.0594 [hep-ph].