Inflation driven by non-linear electrodynamics

Abstract

Abstract We investigate the inflation driven by a nonlinear electromagnetic field based on an NLED lagrangian density $${\mathscr {L}}_{\text {nled}} = - {F} f \left( {F} \right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mtext>nled</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mi>F</mml:mi> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mi>F</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> , where $$f \left( {F}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mi>F</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> is a general function depending on F . We first formulate an f -NLED cosmological model with a more general function $$f \left( {F}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mi>F</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> and show that all NLED models can be expressed in this framework; then, we investigate in detail two interesting examples of the function $$f \left( {F}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mi>F</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> . We present our phenomenological model based on a new Lagrangian for NLED. Solutions to the field equations with the physical properties of the cosmological parameters are obtained. We show that the early Universe had no Big-Bang singularity, which accelerated in the past. We also investigate the qualitative implications of NLED by studying the inflationary parameters, like the slow-roll parameters, spectral index $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , and tensor-to-scalar ratio r , and compare our results with observational data. Detailed phase-space analysis of our NLED cosmological model is performed with and without matter source. As a first approach, we consider the motion of a particle of unit mass in an effective potential. Our systems correspond to fast-slow systems for physical values of the electromagnetic field and the energy densities at the end of inflation. We analyze a complementary system using Hubble-normalized variables to investigate the cosmological evolution before the matter-dominated Universe.

Topics & Concepts