arXiv subjects

Debottam Nandi

Publications and source records attributed to Debottam Nandi.

23 records · Page 2Linked to original sources

arXiv2018

Vector Galileon and inflationary magnetogenesis

Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields cannot be addressed in this framework. The key issue for this long-standing problem is the conformal invariance of the electromagnetic (EM) field in 4-D. While many approaches have been proposed in the literature for breaking conformal invariance of the EM action, here, we provide a completely new way of looking at the modifications to the EM action and generation of primordial magnetic fields during inflation. We explicitly construct a higher derivative EM action that breaks conformal invariance by demanding three conditions - theory be described by vector potential $A_μ$ and its derivatives, Gauge invariance be satisfied, and equations of motion be linear in second derivatives of vector potential. The unique feature of our model is that appreciable magnetic fields are generated at small wavelengths while tiny magnetic fields are generated at large wavelengths that are consistent with current observations.

astro-ph.CO↗

arXiv2017

Hamiltonian formalism of cosmological perturbations and higher derivative theories

The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence of two approaches --- action and order-by-order gravity equation approach --- for cosmological perturbation theory, and establish that both lead to equivalent results for any gravity models at any order of perturbations. We then focus on Hamiltonian formalism that has not been studied extensively in the literature. We provide a generalized Hamiltonian approach for cosmological perturbations which is equivalent to the Lagrangian approach. We show that, the approach can be applied to any model at any order of perturbations. Using this approach, we show that evaluating interaction Hamiltonian is simpler and efficient than earlier approach. In the next work, we concentrate on generalized non-canonical scalar field and by introducing a new variable provide a technique to write Hamiltonian for generalized non-canonical scalar field. We then implement our Hamiltonian approach for non-canonical scalar field and evaluate interaction Hamiltonian without slow-roll approximations. Finally, for the first time, we construct a vector Galileon model in curved space-time in which, the field equations do not contain any higher-derivative terms, yet, preserving U(1) gauge-invariance. Conformal invariance is broken in this model which leads to primordial magnetogenesis and we compare the predictions of our model with observations.

gr-qc↗

arXiv2016

Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

gr-qc↗

arXiv2016

'Constraint consistency' at all orders in Cosmological perturbation theory

We study the equivalence of two - order-by-order Einstein's equation and Reduced action - approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' that needs to be satisfied. We propose a quick and efficient method to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all `constraint' inconsistent models have higher order Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint lapse function and shift vector, though it may have Ostrogradsky's instabilities. We also obtain the single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.

gr-qc↗

arXiv2016

Complete Hamiltonian analysis of cosmological perturbations at all orders

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in the Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al [2006]) for extracting higher order correlations and show that our approach is quick and robust and can be applied to any model of gravity and matter fields.

gr-qc↗