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Register a new userObservational constraint on the varying speed of light theory
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The varying speed of light (VSL) theory is controversial. It succeeds in explaining some cosmological problems, but on the other hand it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devote ourselves to test whether the speed of light is varying from the observational data of the type Ia Supernova, Baryon Acoustic Oscillation, Observational $H(z)$ data and Cosmic Microwave Background (CMB). We select the common form $c(t)=c_0a^n(t)$ with the contribution of dark energy and matter, where $c_0$ is the current value of speed of light, $n$ is a constant, and consequently construct a varying speed of light dark energy model (VSLDE). The combined observational data show a much trivial constraint $n=-0.0033 pm 0.0045$ at 68.3% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time-variable $c(t)$, we find that the speed of light almost has no variation for redshift $z < 10^{-1}$. For high-$z$ observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of $10^{-2}$. We also introduce the geometrical diagnostic $Om (z)$ to show the difference between the VSLDE and $Lambda$CDM model. The result shows that the current data are difficult to differentiate them. All the results show that the observational data favor the constant speed of light.
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We discuss the constant-roll inflation with constant $epsilon_2$ and constant $bareta$. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of $epsilon_1$. The model with constant $epsilon_2$ is ruled out by the observations at the $3sigma$ confidence level, and the model with constant $bareta$ is consistent with the observations at the $1sigma$ confidence level. The potential for the model with constant $bareta$ is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be slow-roll inflation, the $n_s-r$ results from the constant-roll inflation are not the same as those from the slow-roll inflation even when $baretasim 0.01$.
It is often taken for granted that on board a rotating disk it is possible to operate a QTR{it}{global}3+1 splitting of space-time, such that both lengths and time intervals are QTR{it}{uniquely} defined in terms of measurements performed by real rods and real clocks at rest on the platform. This paper shows that this assumption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams travelling in opposite directions along the rim of the disk; which in turn implies some recently pointed out paradoxical consequences undermining the self-consistency of the Special Theory of Relativity (SRT). A correct application of the SRT solves the problem and recovers complete internal consistency for the theory. As an immediate consequence, it is shown that the Sagnac effect only depends on the non homogeneity of time on the platform and has nothing to do with any anisotropy of the speed of light along the rim of the disk, contrary to an incorrect but widely supported idea.
Four-dimensional cosmological models are studied on a boundary of a five-dimensional Anti-de Sitter (AdS_5) black hole with AdS Reissner-Nordstrom and scalar charged Reissner- Nordstrom black hole solutions, where we call the former a Hairless black hole and the latter a Hairy black hole. To obtain the Friedmann-Robertson-Walker (FRW) spacetime metric on the boundary of the AdS_5 black hole, we employ Eddington-Finkelstein (EF) coordinates to the bulk geometry. We then derive modified Friedmann equations on a boundary of the AdS_5 black hole via AdS/CFT correspondence and discuss its cosmological implications. The late-time acceleration of the universe is investigated in our models. The contributions coming from the bulk side is treated as a dark energy source, and we perform MCMC analyses using observational data. Compared to the LCDM model, our models contain additional free parameters; therefore, to make a fair comparison, we use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to analyze our results. Our numerical analyses show that our models can explain the observational data as reliable as the LCDM model does for the current data.
In this paper we study the observational constraints that can be imposed on the coupling parameter, $hat alpha$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| hat alpha | lesssim 10^{10} ,{rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}, {rm s}$), or the immediate vicinity of stellar-mass black holes ($Mlesssim100, M_{odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $hat alpha$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 lesssim hat alpha lesssim 10^8 , {rm m}^2$.
The scalar-tensor theory can be formulated in both Jordan and Einstein frames, which are conformally related together with a redefinition of the scalar field. As the solution to the equation of the scalar field in the Jordan frame does not have the one-to-one correspondence with that in the Einstein frame, we give a criterion along with some specific models to check if the scalar field in the Einstein frame is viable or not by confirming whether this field is reversible back to the Jordan frame. We further show that the criterion in the first parameterized post-Newtonian approximation can be determined by the parameters of the osculating approximation of the coupling function in the Einstein frame and can be treated as a viable constraint on any numerical study in the scalar-tensor scenario. We also demonstrate that the Brans-Dicke theory with an infinite constant parameter $omega_{text{BD}}$ is a counterexample of the equivalence between two conformal frames due to the violation of the viable constraint.
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