We propose a Hamiltonian formalism for a generalized Friedmann-Roberson-Walker cosmology model in the presence of both a variable equation of state (EOS) parameter $w(a)$ and a variable cosmological constant $Λ(a)$, where $a$ is the scale factor. This Hamiltonian system containing 1 degree of freedom and without constraint, gives Friedmann equations as the equation of motion, which describes a mechanical system with a variable mass object moving in a potential field. After an appropriate transformation of the scale factor, this system can be further simplified to an object with constant mass moving in an effective potential field. In this framework, the $Λ$ cold dark matter model as the current standard model of cosmology corresponds to a harmonic oscillator. We further generalize this formalism to take into account the bulk viscosity and other cases. The Hamiltonian can be quantized straightforwardly, but this is different from the approach of the Wheeler-DeWitt equation in quantum cosmology.
A dynamic correspondence between Bose-Einstein condensates and Friedmann-Lemaître-Robertson-Walker and Bianchi I cosmology with a cosmological constant
We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a co…
We propose and study a semi-classical cosmological system akin to the Newton-Schrödinger equation where matter field evolution is determined by time dependent Schrödinger equation. The resulting dynamics is one where the scale factor self-consistently informs the quantum evolution of the scalar field wave function via the Friedmann equation. We study various potentials, and show that for each case, inflation arises naturally, without fine-tuning, for arbitrary initial wave functions for the scalar field. Furthermore, due to zero-point quantum fluctuations of the scalar field, the equation of s…
Considering Verlinde's entropic gravity proposal, we focus the effects of fermionic $q$ deformation on the Einstein's field equations and Friedmann equations. For this purpose, we represent the thermodynamical properties of the deformed fermion gas model in two-dimensional space. To describe the behavior of the quantum black holes, deformed Einstein field equations are derived with the help of deformed entropy function. Moreover, deformed Friedmann equations are investigated by using Friedmann-Robertson-Walker (FRW) metric. We also present the effective ones of the energy density, the pressure…
Recently, Chamseddine and Mukhanov introduced a higher-derivative scalar-tensor theory which leads to a modified Friedmann equation allowing for bouncing solutions. As we note in the present work, this Friedmann equation turns out to reproduce exactly the loop quantum cosmology effective dynamics for a flat isotropic and homogeneous space-time. We generalize this result to obtain a class of scalar-tensor theories, belonging to the family of mimetic gravity, which all reproduce the loop quantum cosmology effective dynamics for flat, closed and open isotropic and homogeneous space-times.
Loop Quantum Cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of short range repulsive quantum effects at the Planck scale. In this work, we are interested in reproducing the effective Friedmann equation of LQC, by considering a generic $f(R,P,Q)$ theory of gravity, where $R=g^{μν}R_{μν}$ is the Ricci scalar, $P=R_{μν}R^{μν}$, and $Q=R_{αβμν}R^{αβμν}$ is the Kretschmann scalar. An order reduction technique allows us to work in $f(R,P,Q)$ theories which are perturbatively close to General Relativity, and to deduce a modified Friedmann eq…
In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the $(3+1)$-dimensional Friedmann model …
We investigate the cosmological consequences of the modified Friedmann equations when the entropy associated with the apparent horizon, given by Barrow entropy, $S\sim A^{1+δ/2}$, where $0\leqδ\leq1$, represents the amount of the quantum-gravitational deformation of the horizon. We study implications of this model in a flat Friedmann-Robertson-Walker (FRW) universe with/without cosmological constant. Taking the cosmological constant into account, this model can describe the current accelerated expansion, although the transition from deceleration phase to the acceleration phase takes place in t…
We apply quantum gravitational results to spatially unbounded Friedmann universes and try to answer some questions related to dark energy, dark matter, inflation and the missing antimatter.
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of tors…
Brane cosmology from observational surveys and its comparison with standard FRW cosmology
研究了膜上的几种暗能量模型。并在四维Friedmann-Robertson-Walker宇宙学框架下与相应的理论进行了比较。为了约束所考虑的模型的参数，最近的观测数据，包括SNIa视星等测量，重子声学振荡结果，哈勃参数演化数据和物质密度扰动。得到了远程平行理论中所谓的{ \it state finder}参数的显式公式，这可能有助于测试这些模型，并建立环量子宇宙学和膜宇宙学之间的联系。它的结论是，联合分析，因为这里开发的一个允许估计，在一个非常方便的方式，可能的偏差，从标准的弗里德曼-罗伯逊-沃克的真实宇宙宇宙学。
In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expans…
In loop quantum cosmology, polymer quantization is applied to gravity and Schrodinger quantization to matter. This approach misses interesting cosmological dynamics coming from the polymer quantization of matter. We demonstrate this in semiclassical cosmology with a scalar field and pressureless dust: gravity is kept classical, dust is used to fix the time gauge, and polymer quantization effects are isolated in the scalar field. The resulting dynamics shows a period of inflation, both with and without a scalar potential, and the emergence of a classical universe at late times. Since gravity is…
We present, for the first time, the quantization process for the Einstein-aether scalar field cosmology. We consider a cosmological theory proposed as a Lorentz violating inflationary model, where the aether and scalar fields interact through the assumption that the aether action constants are ultra-local functions of the scalar field. For this specific theory there is a valid minisuperspace description which we use to quantize. For a particular relation between the two free functions entering the reduced Lagrangian the solution to the Wheeler-DeWitt equation as also the generic classical solu…
We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which the…
