arXiv subjects

Somnath Mukherjee

Publications and source records attributed to Somnath Mukherjee.

9 recordsLinked to original sources

arXiv2021

An accelerated universe with negative equation of state parameter in Inhomogeneous Cosmology with $k$-essence scalar field

We obtain a scaling relation for spherically symmetric k-essence scalar fields $ϕ(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $ϕ(r,t)=ϕ_{1}(r) + ϕ_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits accelerated expansion i.e.cosmic acceleration driven by negative pressure.

gr-qc↗

arXiv2020

Some studies on k essence Lagrangian

K-essence Lagrangian is studied in the context of an early universe epoch when time is very small. Equation of state parameter as well as deceleration parameter , indicates an accelerated expansion of the universe at an early epoch of time driven by negative pressure generated by dark energy.

physics.gen-ph↗

arXiv2020

k-essence classical Hamiltonian approach for an accelerated expansion of the Universe with $ω\approx-1$

We obtain lagrangian for $k$-essence scalar field $ϕ(r,t)$ with scalar curvature $k$ of Friedmann-Lemaitre-Robertson-Walker (FLRW) metric . Obtained lagrangian has two generalised co-ordinates $ϕ$ and logarithm of scale factor ($q=\ln a$). Classical Hamiltonian $({\mathcal H})$ is obtained in terms of two corresponding conjugate momentum $p_{q}$ and $p_ϕ$. Solving Hamilton's equation of motion , we obtain classical solution for scale factor $a(t)$, energy density $ρ$, equation of state parameter $ω$ and deceleration parameter $q_{0}$ . At late time as $t\rightarrow\infty$, we have an exponential growth of scale factor with time, energy density $ρ$ becomes constant, which we can identify as dark energy density, equation of state parameter becomes $ω\approx -1$ and deceleration parameter becomes $ q_{0}\approx -1$. All this results indicates an accelerated expansion of universe driven by negative pressure known as dark energy.

physics.gen-ph↗

arXiv2016

Real Time Video Analysis using Smart Phone Camera for Stroboscopic Image

Motion capturing and there by segmentation of the motion of any moving object from a sequence of continuous images or a video is not an exceptional task in computer vision area. Smart-phone camera application is an added integration for the development of such tasks and it also provides for a smooth testing. A new approach has been proposed for segmenting out the foreground moving object from the background and then masking the sequential motion with the static background which is commonly known as stroboscopic image. In this paper the whole process of the stroboscopic image construction technique has been clearly described along with some necessary constraints which is due to the traditional problem of estimating and modeling dynamic background changes. The background subtraction technique has been properly estimated here and number of sequential motion have also been calculated with the correlation between the motion of the object and its time of occurrence. This can be a very effective application that can replace the traditional stroboscopic system using high end SLR cameras, tripod stand, shutter speed control and position etc.

cs.CV↗

arXiv2016

A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar fields

We obtain a scaling relation for spherically symmetric k-essence scalar fields $ϕ(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $ϕ(r,t)=ϕ_{1}(r) + ϕ_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits late time accelerated expansion i.e.cosmic acceleration driven by negative pressure.

gr-qc↗

arXiv2015

f(R) Gravity with k-essence scaling relation and Cosmic acceleration

A modified gravity theory with $f(R)=R^2$ coupled to a dark energy lagrangian $L=-V(ϕ)F(X)$ , $X=\nabla_μϕ\nabla^μϕ$, gives plausible cosmological scenarios when the modified Friedman equations are solved subject to the scaling relation $X (\frac{dF}{dX})^{2}=Ca(t)^{-6}$. This relation is already known to be valid, for constant potential $V(ϕ)$, when $L$ is coupled to Einstein gravity. $ϕ$ is the k-essence scalar field and $a(t)$ is the scale factor. The various scenarios are: (1) Radiation dominated Ricci flat universe with deceleration parameter $Q=1$. The solution for $ϕ$ is an inflaton field for small times. (2) $Q$ is always negative and we have accelerated expansion of the universe right from the beginning of time and $ϕ$ is an inflaton for small times. (3)The deceleration parameter $Q= -5$, i.e. we have an accelerated expansion of the universe. $ϕ$ is an inflaton for small times.(4)A generalisation to $f(R)= R^n$ shows that whenever $n > 1.780$ or $n < - 0.280$ , $Q$ will be negative and we will have accelerated expansion of the universe. At small times $ϕ$ is again an inflaton.

astro-ph.CO↗

arXiv2010

On A Cosmological Invariant as an Observational Probe in the Early Universe

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(ϕ)F(X)$ with $F$ some general function of $X=\nabla_μϕ\nabla^μϕ$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.

astro-ph.CO↗

arXiv2010

The Role of Boolean Function in Fractal Formation and it s Application to CDMA Wireless Communication

In this paper, a new transformation is generated from a three variable Boolean function 3, which is used to produce a self-similar fractal pattern of dimension 1.58. This very fractal pattern is used to reconstruct the whole structural position of resources in wireless CDMA network. This reconstruction minimizes the number of resources in the network and so naturally network consumption costs are getting reduced. Now -a -days resource controlling and cost minimization are still a severe problem in wireless CDMA network. To overcome this problem fractal pattern produced in our research provides a complete solution of structural position of resources in this Wireless CDMA Network.

cs.NI↗

arXiv2008

Logarithm of the scale factor as a generalised coordinate in a lagrangian for dark matter and dark energy

A lagrangian for the $k-$ essence field is set up with canonical kinetic terms and incorporating the scaling relation of [1]. There are two degrees of freedom, {\it viz.},$q(t)= ln\enskip a(t)$ ($a(t)$ is the scale factor) and the scalar field $ϕ$, and an interaction term involving $ϕ$ and $q(t)$.The Euler-Lagrange equations are solved for $q$ and $ϕ$. Using these solutions quantities of cosmological interest are determined. The energy density $ρ$ has a constant component which we identify as dark energy and a component behaving as $a^{-3}$ which we call dark matter. The pressure $p$ is {\it negative} for time $t\to \infty$ and the sound velocity $c_{s}^{2}={\partial p\over\partialρ} << 1$. When dark energy dominates, the deceleration parameter $Q\to -1$ while in the matter dominated era $Q\sim {1\over 2}$. The equation of state parameter $w={p\over ρ}$ is shown to be consistent with $w={p\overρ}\sim -1$ for dark energy domination and during the matter dominated era we have $w\sim 0$. Bounds for the parameters of the theory are estimated from observational data. Keywords: k-essence models, dark matter, dark energy PACS No: 98.80.-k

gr-qc↗