A note on the Gauge Symmetries of Unimodular Gravity

The symmetries of Unimodular Gravity are clarified somewhat.Comment: 4 pages, v2: acknowledgments correcte

Quantum Corrections to Unimodular Gravity

The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.Comment: 34 page

Big brake singularity is accommodated as an exotic quintessence field

We describe a big brake singularity in terms of a modified Chaplygin gas equation of state p=(\ga_{m}-1)\rho+\al\ga_{m}\rho^{-n}, accommodate this late-time event as an exotic quintessence model obtained from an energy-momentum tensor, and focus on the cosmological behavior of the exotic field, its kinetic energy and the potential energy. At the background level, the exotic field does not blow up whereas its kinetic energy and potential both grow without limit near the future singularity. We evaluate the classical stability of this background solution by examining the scalar perturbations of the metric along with the inclusion of entropy perturbation in the perturbed pressure. Within the Newtonian gauge, the gravitational field approaches a constant near the singularity plus additional regular terms. When the perturbed exotic field is associated with \al>0 the perturbed pressure and contrast density both diverge, whereas the perturbed exotic field and the divergence of the exotic field's velocity go to zero exponentially. When the perturbed exotic field is associated with \al<0 the contrast density always blows up, but the perturbed pressure can remain bounded. In addition, the perturbed exotic field and the divergence of the exotic field's velocity vanish near the big brake singularity. We also briefly look at the behavior of the intrinsic entropy perturbation near the singular event.Comment: 11 pages, no figures. Accepted for its publication in PR

Interacting dark sector with transversal interaction

We investigate the interacting dark sector composed of dark matter, dark energy, and dark radiation for a spatially flat Friedmann-Robertson-Walker (FRW) background by introducing a three-dimensional internal space spanned by the interaction vector $\mathbf{Q}$ and solve the source equation for a linear transversal interaction. Then, we explore a realistic model with dark matter coupled to a scalar field plus a decoupled radiation term, analyze the amount of dark energy in the radiation era and find that our model is consistent with the recent measurements of cosmic microwave background anisotropy coming from Planck along with the future constraints achievable by CMBPol experiment.Comment: To appear in the proceedings of "CosmoSur II - Gravitation and Cosmology in the Southern Cone" (Valparaiso, Chile, 27-31 May 2013

Dark radiation and dark matter coupled to holographic Ricci dark energy

We investigate a universe filled with interacting dark matter, holographic dark energy, and dark radiation for the spatially flat Friedmann-Robertson-Walker (FRW) spacetime. We use a linear interaction to reconstruct all the component energy densities in terms of the scale factor by directly solving the balance's equations along with the source equation. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmic parameters, contrast with the Union 2 sample of supernovae, and analyze the amount of dark energy in the radiation era. It turns out that our model exhibits an excess of dark energy in the recombination era whereas the stringent bound $\Omega_{\rm x}(z\simeq 10^{10})<0.21$ at big-bang nucleosynthesis is fulfilled. We find that the interaction provides a physical mechanism for alleviating the triple cosmic coincidence and this leads to $\Omega_{\rm m0}/\Omega_{\rm x0} \simeq \Omega_{\rm r0}/\Omega_{\rm x0} \simeq {\cal O}(1)$.Comment: 8 pages, 5 figures, 2 tables. Accepted for its publication in The European Physical Journal C (2013). http://link.springer.com/article/10.1140/epjc/s10052-013-2352-7 arXiv admin note: substantial text overlap with arXiv:1210.550

Unimodular Gravity and General Relativity UV divergent contributions to the scattering of massive scalar particles

We work out the one-loop and order $\kappa^2 m_\phi^2$ UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process $\phi + \phi\rightarrow \phi + \phi$ in a $\lambda \phi^4$ theory with mass $m_\phi$. We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contributions in Dimension Regularization. This seems to be at odds with the known result that in a multiplicative MS dimensional regularization scheme the General Relativity corrections, in the de Donder gauge, to the beta function $\beta_{\lambda}$ of the $\lambda$ coupling do not vanish, whereas the Unimodular Gravity corrections, in a certain gauge, do vanish. Actually, we show that the UV divergent contributions to the 1PI Feynman diagrams which give rise to those non-vanishing corrections to $\beta_{\lambda}$ do not contribute to the UV divergent behaviour of the S matrix element of $\phi + \phi\rightarrow \phi + \phi$ and this shows that any physical consequence --such existence of asymptotic freedom due to gravitational interactions-- drawn from the value of $\beta_{\lambda}$ is not physically meaningful.Comment: 13 pages, 4 figure

Nonbaryonic dark matter and scalar field coupled with a transversal interaction plus decoupled radiation

We analyze a universe filled with interacting dark matter, a scalar field accommodated as dark radiation along with dark energy plus a decoupled radiation term within the framework of spatially flat Friedmann-Robertson-Walker (FRW) spacetime. We work in a three-dimensional internal space spanned by the interaction vector and use a transversal interaction $\mathbf{Q_t}$ for solving the source equation in order to find all the interacting component energy densities. We asymptotically reconstruct the scalar field and potential from an early radiation era to the late dominate dark energy one, passing through an intermediate epoch dominated by dark matter. We apply the $\chi^{2}$ method to the updated observational Hubble data for constraining the cosmic parameters, contrast with the Union 2 sample of supernovae, and analyze the amount of dark energy in the radiation era. It turns out that our model fulfills the severe bound of $\Omega_{\rm \phi}(z\simeq 1100)<0.018$ at $2\sigma$ level, is consistent with the recent analysis that includes cosmic microwave background anisotropy measurements from the Atacama Cosmology Telescope and the South Pole Telescope along with the future constraints achievable by Planck and CMBPol experiments, and satisfies the stringent bound $\Omega_{\rm \phi}(z\simeq 10^{10})<0.04$ at $2\sigma$ level in the big-bang nucleosynthesis epoch.Comment: 12 pages plus 5 pages of figures. In order to see the figures go to the journal website (http://link.springer.com/article/10.1140%2Fepjc%2Fs10052-013-2497-4). arXiv admin note: substantial text overlap with arXiv:1303.3356, arXiv:1210.550

Dark matter and Ricci-like holographic dark energy coupled through a quadratic interaction

We examine a spatially flat Friedmann-Robertson-Walker (FRW) universe filled with interacting dark matter and a modified holographic Ricci dark energy (MHRDE). The interaction term is selected as a significant rational function of the total energy density and its first derivative homogeneous of degree. We show that the effective one-fluid obeys the equation of state of a relaxed Chaplygin gas, then the universe turns to be dominated by pressureless dark matter at early times and undergoes an accelerated expansion in the far future driven by a strong negative pressure. Performing a $\chi^{2}$-statistical analysis with the observational Hubble data and the Union2 compilation of SNe Ia, we place some constraints on cosmological parameters analyzing the feasibleness of the modified holographic Ricci ansatz. It turned that MHRDE gets the accelerated expansion faster than the $\Lambda$CDM model. Finally, a new model with a component that does not exchange energy with the interacting dark sector is presented for studying bounds on the dark energy at early times.Comment: 7 pages, 3 figures, conference. To appear in the proceedings of the CosmoSul conference, held in Rio de Janeiro, Brazil, 01-05 august of 201

Dark matter, dark energy, and dark radiation coupled with a transversal interaction

We investigate a cosmological scenario with three interacting components that includes dark matter, dark energy, and radiation in the spatially flat Friedmann-Robertson-Walker universe. We introduce a 3-dimensional internal space, the interaction vector $\mathbf{Q}=(Q_{x}, Q_{m}, Q_{r})$ satisfying the constraint plane $Q_{x}+ Q_{m}+ Q_{r}=0$, the barotropic index vector \boldmath {\gamma}=(\ga_x,\ga_m,\ga_r) and select a transversal interaction vector $\mathbf{Q_t}$ in a sense that \mathbf{Q_t}\cdot \boldmath {\gamma}$=0$. We exactly solve the source equation for a linear $\mathbf{Q_t}$, that depends on the total energy density and its derivatives up to third order, and find all the component energy densities. We obtain a large set of interactions for which the source equation admits a power law solution and show its asymptotic stability by constructing the Lyapunov function. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmic parameters, and analyze the amount of dark energy in the radiation era for the above linear $\mathbf{Q_t}$. It turns to be that our model fulfills the severe bound of $\Omega_{x}(z\simeq 1100)<0.1$ and is consistent with the future constraints achievable by Planck and CMBPol experiments.Comment: 9 pages, 4 figures. Accepted for publication in Physical Review