arXiv subjects

Murli Manohar Verma

Publications and source records attributed to Murli Manohar Verma.

At least 19 recordsLinked to original sources

arXiv2026

Polarization States and Effective Stress Energy Tensor of Gravitational Waves in Metric $f(R)$ Gravity

We investigate the polarization properties and effective stress--energy tensor of gravitational waves in metric $f(R)$ gravity within the linearized approximation around Minkowski spacetime. Owing to the additional scalar degree of freedom inherent in the theory, gravitational waves exhibit polarization states beyond the two tensor modes predicted by general relativity. Using the electric components of the linearized Riemann tensor, we derive explicit expressions for the polarization amplitudes and show that a massless scalar field excites a transverse breathing mode, whereas a massive scalar field generates both breathing and longitudinal responses through a single propagating scalar excitation. Employing the Isaacson high-frequency averaging formalism, we further derive the effective stress--energy tensor and demonstrate that both tensor and scalar perturbations contribute to the total gravitational-wave energy density. The energy transport associated with the massive scalar mode is reduced by its subluminal group velocity, leading to a frequency-dependent suppression of the scalar energy flux. These results establish a unified connection between gravitational-wave polarization and energy transport in metric $f(R)$ gravity and provide potential observational signatures for testing modified gravity with current and future gravitational-wave detectors.

gr-qc↗

arXiv2026

Cosmic Structure Formation in a Viable Power-Law f(R) Gravity Model: Growth Dynamics, Stability, and Observational Signatures

We investigate the evolution of cosmic structures in the power-law modified gravity model $f(R)=R+R^{1+δ}/R_c^δ$, where the dimensionless parameter $δ$ characterizes deviations from General Relativity. The background cosmological dynamics and the evolution of linear matter density perturbations are studied within the framework of metric $f(R)$ gravity. The modified perturbation equation is derived by introducing an effective gravitational coupling associated with the additional scalar degree of freedom, and the evolution of the growth factor, logarithmic growth rate, growth index, and the observable quantity $fσ_8(z)$ are investigated. The results show that the curvature correction enhances the growth of matter perturbations while remaining compatible with the observed late-time accelerated expansion for suitable values of the model parameter. The theoretical viability of the model is established through the ghost-free condition, Dolgov--Kawasaki stability criterion, positive scalaron mass, stable de Sitter solution, and chameleon screening mechanism. Comparison with representative viable $f(R)$ gravity models shows that the present theory achieves a consistent cosmological evolution with a single deviation parameter. The predicted modifications in the growth of structures and the effective gravitational coupling provide observable signatures that can be tested by forthcoming large-scale structure and weak-lensing surveys, providing a means to test curvature-induced modifications of gravity.

physics.gen-ph↗

arXiv2025

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity

Black hole shadows are a widespread topic in astrophysics. This paper searches for an optical view of the black hole and the relationship between black hole shadow and photon sphere with curvature. We were inspired by the observations of Sagittarius $A^*$ and supermassive black hole M87$*$ through the Event Horizon Telescope. We have found the signature of the modified theory of gravity on the photon sphere and shadow. We considered $f(R)$ modified theory of gravity and new scalar degree of freedom $F$ appears in the expressions of photon sphere and shadow.

gr-qc↗

arXiv2024

Scalar modes of polarization and speed of gravitational waves in $f(R)$ gravity

We explore the gravitational waves (GWs) within the framework of the $f(R)$ gravity model represented by $f(R)=R^{1+δ}/R^δ_c$ in the weak field approximation. In this scenario, gravitational waves exhibit an additional polarization mode beyond the standard transverse-traceless (TT) tensor modes. We show that the polarization characteristics of these waves are connected to the scalaron mass and the effective potential derived from the function $f(R)$. Furthermore, the study of the speed of gravitational waves ($c_g$) within the Horndeski theory, particularly using the $f(R)$ model, reveals an intriguing feature about the equality of the speed of gravitational waves to that that of electromagnetic waves. This equivalence arises due to the modification introduced in the Ricci scalar within the $f(R)$ model.

gr-qc↗

arXiv2023

Probing massive gravitons in $f(R)$ with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in $f(R)$ gravity under proper gauge considerations in the shifted Ricci scalar background curvature ($R^{1+ε}$). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on $ε$. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for $ε<<1$. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about $\mathcal{O} (10^{-15})$ eV for $ε<<1 (\approx 10^{-7})$ lensed by ($10^3\leq M_{Lens}\leq 10^6$)$M_\odot$ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.

gr-qc↗

arXiv2022

Effect of the modified gravity on the large scale structure formation

We investigate the formation of the large scale structures in the present accelerated era in $f(R)$ gravity background. This is done by considering the linear growth of matter perturbations at low redshift $z<1$. The effect of $f(R)$ alters the behaviour of the matter density perturbations from the matter dominated universe to the late-time accelerated universe which is encoded in the Newtonian gravitational constant as $G\rightarrow G_{eff}$. The modified gravitational constant ($G_{eff}$) depends on the form of $f(R)$. The late-time accelerated expansion affects the formation of large scale structures by slowing down the growth of matter density. On the other hand, $f(R)$ increases the growth rate of the matter density perturbations. We have found that the source term in $f(R)$ background, $G_{eff}Ω_m$ overcomes the accelerated expansion and the effect of accelerated expansion suppresses the formation of the large scale structures in the asymptotic future.

astro-ph.CO↗

arXiv2022

Unified $f(R)$ gravity at local scales

We explore the shifted $f(R) (\propto R^{1+δ})$ model with $δ$ as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and non-null) along with its conformal analogue is investigated. For null geodesics, we discuss the light deflection angle, whereas for non-null geodesics under the weak field limit, we investigate the perihelion advance of the Mercury orbit in $f(R)$ Schwarzschild background, respectively. The extent of an additional force, appearing for non-null geodesics, depends on $δ$. Such phenomenological investigations allow us to strictly constrain $δ$ to be approximately $\mathcal{O}(10^{-6})$ with a difference of unity in orders at galactic and planetary scales and seems to provide a unique $f(R)$ at local scales. Further, at late cosmic time, we analyse the constraint on $δ$ via the bare scalar self-interaction Einstein frame potential to provide a null test of dark energy. We constrain the deviation parameter, $\midδ\mid$ to $(\approx 0.6)$ which is in a close agreement with the results obtained through various observations in the Jordan frame by several authors. Our results suggest that the present form of model is suitable for the alternate explanation of dark matter-like effects at local scales, whereas at large scales the deviations grow higher and must be addressed in terms of the accelerated background.

astro-ph.CO↗

arXiv2020

Light deflection angle through velocity profile of galaxies in $f(R)$ model

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law $f(R)$ gravity theory of the type $f(R)\propto R^{1+δ}$ with $δ<<1$ for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + $f(R)$ background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in $f(R)$ frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in $f(R)$ theories) appearing in the effective $f(R)$ rotational velocity profile of a typical galaxy with the model parameter $δ\approx O(10^{-6})$ constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in $f(R)$ background. We also contrast the magnitudes of $f(R)$ lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.

astro-ph.CO↗

arXiv2020

Constraining $f(R)$ model through spectral indices and reheating temperature

We investigate a form of $ f(R) = {R^{1+δ}}/{R_c^δ}$ and study the viability of the model for inflation in the Jordan and the Einstein frames. This model is further analysed by using the power spectrum indices of the inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of $δ$ parameter very close to one ($δ=0.98$), while the reheating temperature $T_{re} \sim 10^{17}$ GeV at $δ=0.98$ is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our model. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck 2018. We also show that the Jordan and the Einstein frames are equivalent when $δ\sim 1 $ by using the scalar spectral index, tensor-to-scalar ratio and reheating temperature.

gr-qc↗

arXiv2019

Extended galactic rotational velocity profiles in $f(R)$ gravity background

An attempt has been made to explore the galactic dynamics via the rotational velocity beyond the Einstein's geometric theory of gravity. It is inspired from the geometric relation obtained in the power law $f(R)$ gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein-Hilbert action (taking $R$ as $f(R)\propto R^{1+δ}$) at the galactic scales for the explanation of cosmological dark matter problem and obtain the contribution of dynamical $f(R)$ background geometry in accelerating the test mass. In the weak field limits, we obtain the effective acceleration of the test mass due to a massive spherically symmetric source in $f(R)$ background and develop an equation for the rotational velocity. We test the viability of the model by tracing the motion of test mass outside the typical galactic visible boundaries without considering any dark matter halo profile. We obtain a nice agreement in the outer regions (up to few tens of kpc beyond the visible boundary) of the typical galaxy by using the known galaxy data.\\ We further explore the galactic dynamics for a galaxy NGC 1052 of which the dark matter deficient galaxies, i.e., DF2 and DF4 are a part (satellite galaxies) and discuss plots of the dynamical feature of rotation curves in $f(R)$ background for the model parameter $δ<<1$ and interpret the results for its satellite galaxies.

gr-qc↗

arXiv2018

Dark matter as scalaron in $f(R)$ gravity models

We explore the scalar field obtained under the conformal transformation of the spacetime metric $g_{μν}$ from the Jordan frame to the Einstein frame in $f(R)$ gravity. This scalar field is the result of the modification in the gravitational part of the Einstein's general relativistic theory of gravity. For $f(R)=\frac{R^{1+δ}}{R_{c}^δ}$, we find the effective potential of the scalar field and calculate the mass of the scalar field particle "scalaron". It is shown that the mass of the scalaron depends upon the energy density of standard matter in the background. The interaction between standard matter and scalaron is weak in the high curvature regime. This linkage between the mass of the scalaron and the background leads to the physical effects of dark matter and is expected to reflect the anisotropic propagation of scalaron in moving baryonic matter fields as in merging clusters (Bullet cluster, the Abell 520 system, MACS etc.). Such scenario also satisfies the local gravity constraints of $f(R)$ gravity. We further calculate the equation of state of the scalar field in the action-angle variable formalism and show its distinct features as the dark matter and dark energy with respect to energy density of the scalar field at different values of the model parameter $δ$.

gr-qc↗

arXiv2017

Cosmological wheel or the arrow of time: A classical versus quantum perspective of gravity

It is shown that the structures in the universe can be interpreted to show a closed wheel of time, rather than a straight arrow. An analysis in $f(R)$ gravity model has been carried out to show that due to local observations a small arc at any given spacetime point would invariably indicate an arrow of time from past to future, though on a quantum scale it is not a linear flow but a closed loop, a fact that can be examined through future observations.

physics.gen-ph↗

arXiv2017

Dynamics of $f(R)$ gravity models and asymmetry of time

We solve the field equations of modified gravity for $f(R)$ model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase space analysis of $f(R)$ models, both with and without the effects of radiation. Stability of these points is studied against perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analysing the dynamics of the system during the radiation, matter and acceleration dominated phases of the universe. Certain linear and quadratic forms of $f(R)$ are determined from the geometrical and physical considerations and the behaviour of the scale factor is found for those forms. Further, we also determine the Hubble parameter $H(t)$, Ricci scalar $R$ for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the $f(R)$ gravity in the Einstein frame that may lead to an arrow of time at a classical level.

gr-qc↗

arXiv2016

Cosmological arrow of time in f(R) gravity

The cosmological arrow of time may be linked to the thermodynamic arrow by second law of thermodynamics. The time asymmetry is also associated with dissipative fluid as Tolman introduced a viscous fluid to generate an arrow of time in cyclic cosmology. An arrow of time in cyclic cosmology has been shown using scalar field.In this work we find out the cosmological arrow of time in f(R) gravity. Here we use the relation between a new scalar field and $f(R)$. The dynamics of this new scalar field may emerge the arrow of time.

physics.gen-ph↗

arXiv2014

The BICEP2 data and a single Higgs-like interacting tachyonic field

It is proposed that the recently announced BICEP2 value of tensor-to scalar ratio $r\sim0.2$ can be explained as containing an extra contribution from the recent acceleration of the universe. In fact this contribution, being robust, recent and of much longer duration (by a large order of magnitude) may dominate the contribution from the inflationary origin. In a possible scenario, matter (dark or baryonic) and radiation etc. can emerge from a single Higgs-like tachyonic scalar field in the universe through a physical mechanism not yet fully known to us. The components interact among themselves to achieve the thermodynamical equilibrium in the evolution of the universe. The field potential for the present acceleration of the universe would give a boost to the amplitude of the tensor fluctuations of gravity waves generated by the early inflation and the net effects may be higher than the earlier PLANCK bounds. In the process, the dark energy, as a cosmological constant decays into creation of dark matter. The diagnostics for the three-component, spatially homogeneous tachyonic scalar field are discussed in detail. The components of the field with perturbed equation of state are taken to interact mutually and the conservation of energy for individual components gets violated. We study mainly the $O_{m}(x)$ diagnostics with the observed set of $H(z)$ values at various redshifts, and the dimensionless state-finders for these interacting components. This analysis provides a strong case for the interacting dark energy in our model.

astro-ph.CO↗

arXiv2013

Cosmic expansion driven by real scalar field for different forms of potential

We discuss the expansion of the universe in the FRLW model assuming that the source of dark energy is either tachyonic scalar field or quintessence. The tachyonic scalar field with exponential and power-law potential (function of homogeneous scalar field $ϕ$) both gives exponential expansion of the universe. It is found that this behaviour is not distinguishable from the quintessence with respect to these potentials.

gr-qc↗

arXiv2012

A new mechanism for dark matter generation from an interacting cosmological constant

We propose an alternative scenario for the dark matter generation from an evolving cosmological constant which interacts with the dominant background in certain intermediate phase of the universe, and relaxes to the observed small value at present. In this way, it is shown that the interaction of the cosmological constant with the radiation or matter might generate the dark matter densities with a varied mass spectrum in the universe with their characteristic arc-like frozen signatures on the Cosmic Microwave Background Radiation (CMBR). This approach also suggests a possible solution to the long standing cosmological constant problem.

astro-ph.CO↗

arXiv2012

Evolution of the equation of state parameters of cosmological tachyonic field components through mutual interaction

We study the perturbed equation of state (EOS) parameters of the cosmological tachyonic scalar field components and their mutual time-dependent interaction. It is shown that the discrete temperature-dependent pattern of the EOS emerges from an initial continuum along the evolution of the universe. This leads to two major components in form of dark energy and dark matter, and also suggests a solution to the cosmological constant problem and the coincidence problem.

astro-ph.CO↗