Varying constants entropic--Λ\LambdaCDM cosmology

We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant $G$ and the speed of light $c$. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data it is found that the Hawking temperature numerical coefficient $\gamma$ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of $O(1)$ and that it is also compatible with zero. Besides, in the entropic scenario we observationally test that the fit of the data is allowed for the speed of light $c$ growing and the gravitational constant $G$ diminishing during the evolution of the universe. We also obtain a bound on the variation of $c$ to be $\Delta c/c \propto 10^{-5} >0$ which is at least one order of magnitude weaker than the quasar spectra observational bound.Comment: Matched with published version. some changes in Section VII, 15 page

General form of entropy on the horizon of the universe in entropic cosmology

Entropic cosmology assumes several forms of entropy on the horizon of the universe, where the entropy can be considered to behave as if it were related to the exchange (the transfer) of energy. To discuss this exchangeability, the consistency of the two continuity equations obtained from two different methods is examined, focusing on a homogeneous, isotropic, spatially flat, and matter-dominated universe. The first continuity equation is derived from the first law of thermodynamics, whereas the second equation is from the Friedmann and acceleration equations. To study the influence of forms of entropy on the consistency, a phenomenological entropic-force model is examined, using a general form of entropy proportional to the $n$-th power of the Hubble horizon. In this formulation, the Bekenstein entropy (an area entropy), the Tsallis--Cirto black-hole entropy (a volume entropy), and a quartic entropy are represented by $n=2$, $3$, and $4$, respectively. The two continuity equations for the present model are found to be consistent with each other, especially when $n=2$, i.e., the Bekenstein entropy. The exchange of energy between the bulk (the universe) and the boundary (the horizon of the universe) should be a viable scenario consistent with the holographic principle.Comment: Final version accepted for publication in PRD. Several pasragraphs and references are added and corrected. [10 pages

Cosmological model from the holographic equipartition law with a modified R\'{e}nyi entropy

Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified R\'{e}nyi entropy is applied to Padmanabhan's `holographic equipartition law', by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original R\'{e}nyi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term.Comment: Final version accepted for publication in EPJC. The titile is revised and references are added. [12 pages, 4 figures

How universe evolves with cosmological and gravitational constants

With a basic varying space-time cutoff $\tilde\ell$, we study a regularized and quantized Einstein-Cartan gravitational field theory and its domains of ultraviolet-unstable fixed point $g_{\rm ir}\gtrsim 0$ and ultraviolet-stable fixed point $g_{\rm uv}\approx 4/3$ of the gravitational gauge coupling $g=(4/3)G/G_{\rm Newton}$. Because the fundamental operators of quantum gravitational field theory are dimension-2 area operators, the cosmological constant is inversely proportional to the squared correlation length $\Lambda\propto \xi^{-2}$. The correlation length $\xi$ characterizes an infrared size of a causally correlate patch of the universe. The cosmological constant $\Lambda$ and the gravitational constant $G$ are related by a generalized Bianchi identity. As the basic space-time cutoff $\tilde\ell$ decreases and approaches to the Planck length $\ell_{\rm pl}$, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point $g_{\rm ir}$, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point $g_{\rm uv}$. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point $g_{\rm uv}$, and its deviation from the $\Lambda$CDM can be examined by low-redshift $(z\lesssim 1)$ cosmological observations, such as supernova Type Ia.Comment: typo corrections, the final version to appear in Nucl. Phys. B (2015). 24 pages and 6 figure