Anisotropic Cosmology and (Super)Stiff Matter in Hořava's Gravity Theory
S. Kalyana Rama
备注：
Version 4: 16 pages. Results unchanged but extensive rearranging, and some addition, of materials. More references added. To be published in Physical Review D
We study anisotropic cosmology in Hořava's gravity theory and obtain Kasner type solutions, valid for any number d of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling λ. Also, Hořava's (super)renormalisable theory predicts (super)stiff matter whose equation of state is p = w ρwith w \ge 1. We discuss briefly the implications of these results for the nature of cosmological collapse.
In this work, we shall incorporate a stiff era in the Universe's evolution in the context of $F(R)$ gravity. After deriving the vacuum $F(R)$ gravity, which may realize a stiff evolution, we combine the stiff $F(R)$ gravity with an $R^2$ model, and we construct a qualitative model for the inflationary and stiff era, with the latter commencing after the end of the inflationary era. We assume that the baryogenesis occurs during the stiff era, and we calculate the baryon to entropy ratio, which effectively constraints the functional form of the stiff $F(R)$ gravity. Further constraints on the sti…
In this work the homogeneous and isotropic Universe of Friedmann-Robertson-Walker is studied in the presence of two fluids: stiff matter and radiation described by the Schutz's formalism. We obtain to the classic case the behaviour of the scale factor of the universe. For the quantum case the wave packets are constructed and the wave function of the universe is found.
In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.
A scenario for gravitational particle creation in a stiff matter dominated flat Friedmann-Robertson-Walker universe is presented. The primary creation of scalar particles is calculated using quantum field theory in curved spacetime and it is found to be strongly dependent on the scalar mass and the expansion parameter of the universe. The particle creation is most effective for a very massive scalar field and large expansion parameter. We apply the results to cosmology and calculate an upper bound for the equilibrium temperature of the secondary particles created by the scalar field decay.
Standard cosmology from the brane cosmology with a localized matter
讨论了5D anti de Sitter Reissner-Nordstrom（AdSRN $_5$）时空中的膜宇宙学.具有张力$σ$的膜被定义为具有质量$M$和电荷$Q$的AdSRN $_5$空间的边缘。在这种情况下，我们从类弗里德曼方程中的$M$和$Q^2$中分别得到了CFT辐射项$(ρ_{CFT})$和带电尘埃$(-ρ^2_{cd})$。然而，该方程是不合理的，因为它包含带负号的$ρ_{cd}^2$ -项。从标准宇宙学的角度来看，这是非常规的。为了解决这个问题，我们引入了一个满足$P_{dm}=0$的局域尘埃物质。如果是$ρ_{dm}=\fr{\sqrt 3}{2}ρ_{cd}$，则不需要的$-ρ_{cd}^2$与$ρ_{dm}^2$抵消，从而恢复了具有CFT辐射和尘埃物质的标准Friedmann-Robertson-Walker宇宙。考虑到刚性问题，我们可以将$ρ_{csti}\sim Q^2$设置为负号。在这里，我们引入一个无质量标量，它扮演着一个刚性物质的角色与$P_{sca}=ρ_{sca}$取消$-ρ_{csti}$。然而，在这种情况下，我们发现了标准宇宙学和膜宇宙学的混合版本。
The exact renormalization group flow equations for gravity lead to quantum corrections of Newton's constant and cosmological constant. Using this we investigate the Bianchi-I cosmological model at late times. In particular, we obtain the scale factors in different directions, and observe that they eventually evolve into Friedmann-Lemaître-Robertson-Walker (FLRW) universe for radiation. However, for stiff matter the universe shows a Kasner like behaviour. The presentation is based on our work published in \cite{Mandal:2019xlg}.
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic s…
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher derivatives of the matter energy density and pressure. For the cases of dust, radiation, and stiff matter we analyze the cosmological behavior, finding accelerating, de Sitter, and non-accelerating p…
The Self-Gravitational Corrections as the Source for Stiff Matter on the Brane in $SAdS_5$ Bulk
一个具有非零能量密度的$D3-$膜被认为是五维Schwarzschild anti de Sitter体背景的边界。考虑到自引力效应对黑洞熵的半经典修正，利用AdS/CFT对应，得到了第一类Friedmann方程的自引力修正.由于自引力效应，哈勃方程中的附加项为$a^{-6}$。因此，自引力修正作为刚性物质的来源，这与标准FRW宇宙学相反，在标准FRW宇宙学中，黑洞的电荷起着这种作用。
In Hořava-Lifshitz cosmology we use the holographic Ricci-like cut-off for the energy density proposed by L. N. Granda and A. Oliveros and under this framework we study, through the cosmic evolution at late times, the sign change in the amount of non-conservation energy ($Q$) present in this cosmology. We revise the early stage (curvature-dependent) of this cosmology, where a term reminiscent of stiff matter is the dominant, and in this stage we find a power-law solution for the cosmic scale factor although $ω=-1$. Late and early phantom schemes are obtained without requiring $ω<-1$. Neverthel…
We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton's constant $G$ and cosmological constant $Λ$. We have considered the solutions of the flow equations for $G$ and $Λ$ at next to leading order in the infrared cutoff scale. Using these scale dependent $G$ and $Λ$ in Einstein equations for the Bianchi-I model, we obtain the scal…
The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Horava cosmology. Special attention is paid to the analysis o…
We study the holographic dark energy on the subject of Ho$\check{r}$ava-Lifshitz gravity with a time dependent gravitational constant (G(t)), in the non-flat space-time. We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant. we find out a relation for the state parameter of the dark energy equation to low redshifts which containing varying $G$ correction.
Horava and Melby-Thompson recently proposed a new version of the Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated by introducing a Newtonian pre-potential $ϕ$ and a local U(1) gauge field $A$. In this paper, we first derive the corresponding Hamiltonian, super-momentum constraints, the dynamical equations, and the equations for $ϕ$ and $A$, in the presence of matter fields. Then, we apply the theory to cosmology, and obtain the modified Friedmann equation and the conservation law of energy, in addition to the equations for $ϕ$ and $A$. When the spatial curvature is…
Quantum cosmology of the Friedmann-Lemaître-Robertson-Walker model with cosmological constant in the Ho$\check{\rm r}$ava-Lifshitz type gravity is studied in the phase space by means of the Wigner function. The modification of the usual general relativity description by the Ho$\check{\rm r}$ava-Lifshitz type gravity induces a new scenario for the origin of the Universe with an embryonic era where the Universe can exist classically before the tunneling process takes place and which gives rise to the current evolution of the Universe. The Wigner functions corresponding to the Hartle-Hawking, Vil…
Among the available quantum gravity proposals, string theory, loop quantum gravity, non-commutative geometry, group field theory, causal sets, asymptotic safety, causal dynamical triangulation, emergent gravity are among the best motivated models. As an introductory summary to this special issue of Comptes Rendus Physique, I explain how those different theories can be tested or constrained by cosmological observations.
The modified field equations are written in logarithmic and power law versions of entropy corrected models in Einstein's gravity in the background of FRW universe. In one section, a brief review of the Ho$\check{\text r}$ava-Lifshitz gravity is discussed and the modified field equations in logarithmic and power law versions of entropy corrected models in Ho$\check{\text r}$ava-Lifshitz gravity are formulated. The stability analysis for these models are performed by describing the dynamical system. In another section, a brief review of the fractal universe is presented and the modified field eq…
