Energy Conditions in Symmetric Teleparallel Gravity
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Mandal, Sanjay
A complete theory of gravity impels us to go beyond Einstein's General Relativity. One promising approach lies in a new class of teleparallel theory of gravity named f (Q), where the nonmetricity Q is responsible for the gravitational interaction. The important roles any of these alternative theories should obey are the energy condition constraints. Such constraints establish the compatibility of a given theory with the causal and geodesic structure of space-time. In this work, we present a complete test of energy conditions for f (Q) gravity models. The energy conditions allowed us to fix our free parameters, restricting the families of f (Q) models compatible with the accelerated expansion our Universe passes through. Our results straight the viability of f (Q) theory, leading us close to the dawn of a complete theory for gravitation.
 Hello everyone, this is Sanjay Mandal from Department of Mathematics of Birla Institute of Technology and Science, Hyderabad, India. So firstly I would like to thank the organizers of International Selection of Physics 2020 for giving us an opportunity to present our work. Now I am going to talk about on the topic energy conditions in symmetric telephoral gravity. As we know so far the Einstein theory of relativity was a successful theory and it has also passed so many observations like LIGO, VIRGO and the black hole image from the event horizontal discourse and it was very fundamental and successful theory so far. Also besides this there are some alternative theory like teleparallel gravity and symmetric teleparallel gravity. Here in this paper we have studied the symmetric teleparallel gravity and we basically focused on the its energy condition and it has come to the motion equation we have taken the action as presented in equation 1 also we have taken the perfect fluid for the matter and the FLRW metric and for this FLRW metric and the non-metric city term Q which is represented the motion equation in symmetric teleparallel gravity which takes equal to Q is equal to 6 h square and using equation 1, 2 and 3 we got the motion equations 4 and 5 and again we reorder 4 and 5 in analogy with GR we got the 3 h square is equal to here rho delta and phi delta represent the effective pressure and density of air model and as we know energy condition is an important tool to study the time leg space like and the light leg of behavior of air universe and in order to study the energy condition first we found the weak energy condition, non-energy condition and domain energy condition using the standard GR condition and we got the and collaborating with the work of capiculo we found the strong energy condition as to this equation 10 as we know the cosmological parameter such as Hubble parameter and deceleration parameter, jerk parameter, snag parameter can be written like this and also we using equation 11 we reorder it into s dot and s double dot and from using 12 and 13 we found the expression for all the energy condition like strong energy condition, non-energy, weak energy and dominant energy condition after that we know to study some cosmological model we have taken the first case as a algebraic function of q and then in order to constrain the model parameter same and we have taken here the present observational values of s naught and q naught from flank data and another proper as you can see here energy density, weak energy condition, dominant energy condition satisfied whereas the strong energy condition violated and which is represent and which is an agreement with the present scenario for universe for our second model we have taken fq as a logarithmic function and you can see this paper which is published in physical review recently and in order to compare our model with lambda c dm model here we have compared and as you can know the fq is equal to minus q represent the lambda c dm model and here we have expressed the energy condition if one can see this if you put the present value of Hubble parameter and this repulation parameter at that stage the strong energy condition will how let and other will be satisfied and also this is an agreement with our like our model which satisfied the lambda c dm model and as you can see know the Planck collaboration and lambda c dm model present the present cosmological scenario with the value of equation of state parameter as omega nearly equal to minus 1 here also we have presented our omega for our model as you can see it is very nearly close to minus 1 and slightly debuted because of its modification and here are we found some conclusions like we have constrained the model parameter same n against the observational data which shows the accelerator expansion of the universe and it is compactable with the lambda c dm as well as the observational data and this result allow us to be higher value of the different familiar of q models and here are some references and thank you so much for your kind attention.
 Hello everyone, this is Sanjay Mandal from Department of Mathematics of Birla Institute  of Technology and Science, Hyderabad, India.  So firstly I would like to thank the organizers of International Selection of Physics 2020  for giving us an opportunity to present our work.  Now I am going to talk about on the topic energy conditions in symmetric telephoral  gravity.  As we know so far the Einstein theory of relativity was a successful theory and it has also passed  so many observations like LIGO, VIRGO and the black hole image from the event horizontal  discourse and it was very fundamental and successful theory so far.  Also besides this there are some alternative theory like teleparallel gravity and symmetric  teleparallel gravity.  Here in this paper we have studied the symmetric teleparallel gravity and we basically focused  on the its energy condition and it has come to the motion equation we have taken the action  as presented in equation 1 also we have taken the perfect fluid for the matter and the FLRW  metric and for this FLRW metric and the non-metric city term Q which is represented the motion  equation in symmetric teleparallel gravity which takes equal to Q is equal to 6 h square  and using equation 1, 2 and 3 we got the motion equations 4 and 5 and again we reorder 4 and  5 in analogy with GR we got the 3 h square is equal to here rho delta and phi delta represent  the effective pressure and density of air model and as we know energy condition is an important  tool to study the time leg space like and the light leg of behavior of air universe  and in order to study the energy condition first we found the weak energy condition,  non-energy condition and domain energy condition using the standard GR condition and we got  the and collaborating with the work of capiculo we found the strong energy condition as to  this equation 10 as we know the cosmological parameter such as Hubble parameter and deceleration  parameter, jerk parameter, snag parameter can be written like this and also we using  equation 11 we reorder it into s dot and s double dot and from using 12 and 13 we found  the expression for all the energy condition like strong energy condition, non-energy,  weak energy and dominant energy condition after that we know to study some cosmological  model we have taken the first case as a algebraic function of q and then in order to constrain  the model parameter same and we have taken here the present observational values of  s naught and q naught from flank data and another proper as you can see here energy  density, weak energy condition, dominant energy condition satisfied whereas the strong energy  condition violated and which is represent and which is an agreement with the present  scenario for universe for our second model we have taken fq as a logarithmic function  and you can see this paper which is published in physical review recently and in order to  compare our model with lambda c dm model here we have compared and as you can know the fq  is equal to minus q represent the lambda c dm model and here we have expressed the energy  condition if one can see this if you put the present value of Hubble parameter and this  repulation parameter at that stage the strong energy condition will how let and other will  be satisfied and also this is an agreement with our like our model which satisfied the  lambda c dm model and as you can see know the Planck collaboration and lambda c dm model  present the present cosmological scenario with the value of equation of state parameter  as omega nearly equal to minus 1 here also we have presented our omega for our model  as you can see it is very nearly close to minus 1 and slightly debuted because of its  modification and here are we found some conclusions like we have constrained the model parameter  same n against the observational data which shows the accelerator expansion of the universe  and it is compactable with the lambda c dm as well as the observational data and this  result allow us to be higher value of the different familiar of q models and here are  some references and thank you so much for your kind attention.
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