General Relativity and Quantum Cosmology (gr-qc)

Abstract: We investigate the cosmological implications of $f(Q)$ gravity, which is a modified theory of gravity based on non-metricity, in non-flat geometry. We perform a detailed dynamical-system analysis keeping the $f(Q)$ function completely arbitrary. As we show, the cosmological scenario admits a dark-matter dominated point, as well as a dark-energy dominated de Sitter solution which can attract the Universe at late times. However, the main result of the present work is that there are additional critical points which exist solely due to curvature. In particular, we find that there are curvature-dominated accelerating points which are unstable and thus can describe the inflationary epoch. Additionally, there is a point in which the dark-matter and dark-energy density parameters are both between zero and one, and thus it can alleviate the coincidence problem. Finally, there is a saddle point which is completely dominated by curvature. In order to provide a specific example, we apply our general analysis to the power-law case, showing that we can obtain the thermal history of the Universe, in which the curvature density parameter may exhibit a peak at intermediate times. These features, alongside possible indications that non-zero curvature could alleviate the cosmological tensions, may serve as advantages for $f(Q)$ gravity in non-flat geometry.

Abstract: We apply quadratic $f(R)=R+\epsilon R^2$ field equations, where $\epsilon$ has a dimension [L$^2$], to static spherical stellar model. We assume the interior configuration is determined by Krori-Barua ansatz and additionally the fluid is anisotropic. Using the astrophysical measurements of the pulsar PSR J0740+6620 as inferred by NICER and XMM observations, we determine $\epsilon\approx \pm 3$ km$^2$. We show that the model can provide a stable configuration of the pulsar PSR J0740+6620 in both geometrical and physical sectors. We show that the Krori-Barua ansatz within $f(R)$ quadratic gravity provides semi-analytical relations between radial, $p_r$, and tangential, $p_t$, pressures and density $\rho$ which can be expressed as $p_r\approx v_r^2 (\rho-\rho_1)$ and $p_r\approx v_t^2 (\rho-\rho_2)$, where $v_r$ ($v_t$) is the sound speed in radial (tangential) direction, $\rho_1=\rho_s$ (surface density) and $\rho_2$ are completely determined in terms of the model parameters. These relations are in agreement with the best-fit equations of state as obtained in the present study. We further put the upper limit on the compactness, which satisfies the $f(R)$ modified Buchdahl limit. Interestingly, the quadratic $f(R)$ gravity with negative $\epsilon$ naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or $f(R)$ gravity with positive $\epsilon$ where the compactness can arbitrarily approach the black hole limit $C\to 1$. The model predicts a core density a few times the saturation nuclear density $\rho_{\text{nuc}} = 2.7\times 10^{14}$ g/cm$^3$, and a surface density $\rho_s > \rho_{\text{nuc}}$. We provide the mass-radius diagram corresponding to the obtained boundary density which has been shown to be in agreement with other observations.

Abstract: In this work we study the cosmological perturbations in Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, i.e. the teleparallel analog of Horndeski gravity. In order to understand the evolution of structure in a cosmological model, it is necessary to study its cosmology not only in the background but also perturbatively. Both Horndeski and its teleparallel analog have been analyzed a lot in the literature, but in order to study them quantitatively, we need to know their cosmological perturbations. That is why, we study here the scalar-vector-tensor decomposition of the theory and we also express the so-called alpha parameters in terms of the arbitrary functions of the theory, that designate the deviation from the {\Lambda}CDM model. We have explored tensor, vector and scalar perturbation of the action up to second order, which drastically opens up new possibilities on searches in the parameter space of scalar-tensor theories in the context of observations.

Abstract: The nanohertz stochastic gravitational wave background (SGWB) is an excellent early universe laboratory for testing the fundamental properties of gravity. In this letter, we elucidate on the full potential of pulsar timing array (PTA) by utilizing cosmic variance-limited, or rather experimental noise-free, correlation measurements to understand the SGWB and by extension gravity. We show that measurements of the angular power spectrum play a pivotal role in the PTA precision era for scientific inferencing. In particular, we illustrate that cosmic variance-limited measurements of the first few power spectrum multipoles enable us to clearly set apart general relativity from alternative theories of gravity.

Abstract: We present an analytic method for calculating the tidal response function of a non-rotating and a slowly rotating black hole from the Teukolsky equation in the small frequency and the near horizon limit. We point out that in the relativistic context, there can be two possible definitions of the tidal Love number and the dissipative part that arise from the tidal response function. Our results suggest that both of these definitions predict zero tidal Love number for a non-rotating black hole. On the other hand, for a slowly rotating black hole in a generic tidal environment, these two definitions of the tidal Love number do not coincide. While one procedure suggests a zero tidal Love number, the other procedure gives a purely imaginary tidal Love number. As expected, the dissipative terms differ as well. We emphasize that in our analysis we keep all the terms linear in the frequency, unlike previous works in the literature. Following this, we propose a procedure to calculate the tidal response function and hence the Love number for an arbitrarily rotating black hole.