This paper is aimed to study the group invariant solutions of the evolution equations in Brans-Dicke cosmology. In this context, we have considered the flat homogeneous Brans-Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model and have used Lie and Noether symmetry on the augmented system. From Lie symmetry we have determined the unknown potential for two different values of the equation of state parameter w. Then assuming that the Lagrangian admits a Noether symmetry, an analytic solution of the system is obtained in both old and new coordinate systems. © 2018 World Scientific Publishing Company.

S DUTTA

S MONDAL

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Lie and Noether symmetry analysis in Brans-Dicke cosmology

Modern Physics Letters A

The paper deals with a non-minimally coupled scalar field in the background of homogeneous but anisotropic Kantowski–Sachs space–time model. The form of the coupling function of the scalar field with gravity and the potential function of the scalar field are not assumed phenomenologically, rather they are evaluated by imposing Noether symmetry to the Lagrangian of the present physical system. The physical system gets considerable mathematical simplification by a suitable transformation of the augmented variables (a,b,ϕ)→(u,v,w) and by the use of the conserved quantities due to the geometrical symmetry. Finally, cosmological solutions are evaluated and analyzed from the point of view of the present evolution of the Universe. © 2018 Elsevier Inc.

Journal	Modern Physics Letters A
Publisher	World Scientific Publishing Co. Pte Ltd
ISSN	0217-7323