Figure 4 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Cosmological solutions for the scale parameter a from the modified Friedmann equations. This figure displays the solution for the radiation equation of state and positive \(\beta '\). See the text for more explanation
Source publication
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior o...
Similar publications
We live in exciting times of ground breaking discoveries in physics and astronomy! Recent detections of gravitational waves predicted by Albert Einstein a century ago have once again confirmed his powerful theory of General Relativity for describing the shape and evolution of the Universe. Gravitational waves open up a new window to view novel astr...
Citations
... In recent times, this approach is used to study the implication of quantum corrections to the Newtonian potential on the Friedmann equation and, thus, on the evolution of the universe [9,10]. The quantum corrections to the Newtonian potential calculated using an effective field theory approach were used to set up the Friedmann equation in [9,10]. ...
... In recent times, this approach is used to study the implication of quantum corrections to the Newtonian potential on the Friedmann equation and, thus, on the evolution of the universe [9,10]. The quantum corrections to the Newtonian potential calculated using an effective field theory approach were used to set up the Friedmann equation in [9,10]. In these works, the variation in scale factor with time was used to investigate the evolution of the universe. ...
... In these works, the variation in scale factor with time was used to investigate the evolution of the universe. The construction of the Friedmann equation, incorporating a quantum correction to the Newtonian potential, and analyzing the time evolution of the scale factor provides valuable insights [9,10]. These studies also help us achieve a better understanding of quantum corrections, and these can lead to clues for quantum gravity. ...
Considering space-time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to κ-deformed space-time, we derive the modified Friedmann equations, valid up to the first order, in the deformation parameter. Analyzing these deformed equations, we derive the time evolution of the scale factor in cases of radiation-dominated, matter-dominated, and vacuum (energy)-dominated universes. We show that the rate of change of the scale factor in all three situations is modified by the non-commutativity of space-time, and this rate depends on the sign of the deformation parameter, indicating a possible explanation for the observed Hubble tension. We undertake this investigation for two different realizations of non-commutative space-time coordinates. In both cases, we also argue for the existence of bounce in the evolution of the universe.
... We begin with the classic derivation of the Friedmann equations, then repeat the same feat with a modified potential and at the end, we study the behaviour of the scale factor using the critical constant model and a different method. In the derivation of the Friedmann equations with and without the quantum correction, as well as in the critical density analysis, we follow [40]. ...
... This completes the derivation of the two Friedmann equations in the framework of Newtonian mechanics. It should be noted that this is not the only way to arrive at the equations and different approaches have been proposed [40]. ...
... We mention this explicitly since it seems that this is a decisive point on deciding the sign of γ q which is, in turn, important for the behaviour of the scale factor. We display some of the most recent values in the table below [40]: With this new potential, the total energy will be described by ...
The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections and a non-flat universe with bulk viscosity. Within these models, we probe into the initial singularity by using different techniques. Several nonsingular universes emerge, one of the possibilities being a static non-expanding and stable Einstein universe.
... Here corrections proportional toh have been calculated and confirmed [9,10]. They have applications in quantum corrections to the Schwarzschild metric and cosmology [11,12]. ...
We consider the non-linear classical field theory which results from adding to the Maxwell's Lagrangian the contributions from the weak-field Euler-Heisenberg Lagrangian and a non-uniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the modified Gauss law, resulting in a higher order differential equation. This equation gives the electric field produced by stationary charges in the higher order non-linear electrodynamics. Specializing for the case of a point charge, we investigate the solutions of the modified Gauss law and calculate the correction to the Coulomb law.
... Otherwise, it is more involved than by merely adding quantum corrections to the Newtonian potential. 25 Thus, we will consider different epochs of the early universe, where the involved energies are lower but its scale is small enough in order to use a quantum approach by taking the Schrödinger equation into consideration. In this scenario, the galaxies have not emerged yet, but their seeds have. ...
We obtain the wave functions associated with the quantum Newtonian universe with a cosmological constant which is described by the Schrödinger equation and discuss some aspects of its dynamics for all forms of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence. These wave functions of the quantum Newtonian universe are obtained in terms of Heun’s functions and the respective energy levels are shown. We use these solutions to investigate the expansion of the universe and found that the asymptotic behavior for the scale factor is R ∼ et for whatever the form of energy density is. We also analyze the behavior of the universe at early stages.
... The other is the choice of the inflationary scenario at the beginning of the universe. Many solutions for both problems have been suggested including scalar fields [9] and higher order gravity [10][11][12] for the inflationary mechanism and versions of quantum gravity [13][14][15] or quantum corrected cosmology [16] for the first problem . ...
We probe into universes filled with Quark Gluon Plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the Quark Gluon Plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor R(t) which goes to zero only asymptotically. We further extend the model of bulk viscosity to include a Cosmological Constant. We contrast the previous results with the cosmology of universes with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann-Lama\^itre-Robertson-Walker metric. To this end we use a version of the energy-momentum tensor from the M\"uller-Isreal-Stewart theory which leads to causal Navier-Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges non-singular.
... This suggests that the Hubble parameter can have a local minimum, a sign of a bouncing universe. Such forms appear in theories such as Loop Quantum Cosmology models [63], Generalized Uncertainty Principle approaches [64] or quantum corrections in Newtonian Cosmology [65]. ...
Cosmologies based on General Relativity encompassing an anti-symmetric connection (torsion) can display nice desirable features as the absence of the initial singularity and the possibility of inflation in the early stage of the universe. After briefly reviewing the standard approach to the cosmology with torsion, we generalize it to demonstrate that several theories of torsion gravity are possible using different choices of the diffeomorphic invariants in the Lagrangians. As a result, distinct cosmologies emerge. In all of them it is possible that the universe avoids the initial singularity and passes through an initial accelerated expansion. Differences between these theories are highlighted.
We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order O(G2) in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic conservation of kinetic energy and potential energy for an infinitesimal mass. We then consider the leading classical correction term and the quantum correction term in the Newtonian potential for deriving the Friedmann equation, however, the quantum correction term is too small and hence does not contribute in the physical results. We then investigate the difference in scale factor with the usual scale factor for various matters like radiation, dust and cosmological constant by considering the corrections in the Newtonian potential. We observe that the evolution of the universe is similar for radiation and dust cases at late times. The cosmological constant case shows a steep increase in the scale factor compared to the other cases. We also note that the universe may have a bounce in the case of radiation depending on the sign of the coefficient of the leading classical correction.
The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections and a non-flat universe with bulk viscosity. Within these models, we probe into the initial singularity by using different techniques. Several nonsingular universes emerge, one of the possibilities being a static non-expanding and stable Einstein universe.
We consider the nonlinear classical field theory which results from adding to the Maxwell’s Lagrangian the contributions from the weak-field Euler–Heisenberg Lagrangian and a nonuniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the modified Gauss law, resulting in a higher-order differential equation. This equation gives the electric field produced by stationary charges in the higher-order nonlinear electrodynamics. Specializing for the case of a point charge, we investigate the solutions of the modified Gauss law and calculate the correction to the Coulomb law.
We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann–Lamaître–Robertson–Walker metric. To this end we use a version of the energy–momentum tensor from the Müller–Israel–Stewart theory which leads to causal Navier–Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.
