On a dark energy model explicitlyOn a dark energy model explicitlyparametrised by the deceleration parameterparametrised by the deceleration parameter

Martiros KhurshudyanMartiros Khurshudyan

University of Science and Technology of ChinaUniversity of Science and Technology of China

On a dark energy model explicitlyOn a dark energy model explicitlyparametrised by the deceleration parameterparametrised by the deceleration parameter

Short introduction – known facts Short introduction – known facts Gaussian Processes (with Gaussian Processes (with H(z) data)H(z) data)

some applicationssome applications

Our Dark Energy model and GP Our Dark Energy model and GP Some resultsSome results ConclusionConclusion

Short introduction – known facts Short introduction – known facts

Large scale universeDark energy has enough negative pressure to workagainst gravity.

Dark matter is going to be something having attractivenature.

Models of dark energy – cosmological constant(thefirst dark energy model), varying cosmologicalconstant models, quintessence, phantom, k-essence(scalar field representations), ghost dark energy,holographic dark energy (the energy density isparametrised), Chaplygin gas (dark energy and darkmatter joint model with a non-linear EoS)…

Alternative approach

a modification of gravity

(I will skip the discussion on this issue becausethe community is very well familiar with thisidea)

Gaussian processes (with Gaussian processes (with H(z) data)H(z) data)

The covariance function (kernel) whichcorrelates the function H(z) at different points

The Gaussian distribution presents a distributionof a random variable characterized by a meanand a covariance.

GP should be understood as a distribution overfunctions, characterized by a mean function anda covariance matrix.

Marina Seikel, Chris Clarkson, Mathew Smith, JCAP 06 (2012), 036

Ming-Jian Zhang, Jun-Qing Xia, JCAP 1612 (2016) no.12, 005

We use GaPP code by Marina Seikel et al...

Gaussian processesGaussian processes

Gaussian processesGaussian processes

Gaussian Processes (with Gaussian Processes (with H(z) data) - some applicationsH(z) data) - some applications

How we can use GP with IDE?

It is very simple task if EoS of DE is given

eventually the interaction term Q will beexpressed as a function of EoS of DE, theHubble parameter and its higher order derivatives

How we can use GP in case of CC?

Gaussian Processes (with Gaussian Processes (with H(z) data) - some applicationsH(z) data) - some applications

It is very simple task if EoS of DE is given andthe form of the particle creation is assumed

eventually the interaction term Q will beexpressed as a function of EoS of DE, theHubble parameter and its higher order derivativesand other parameters describing the particlecreation rate

How we can use GP in cosmology with particle creation when we have IDE ?

Our Dark Energy model and GP Our Dark Energy model and GP

Motivation of the research Our dark energy model

The main results obtained from direct numerical integration

But this is fully model dependent result!!!!!

q is the deceleration parameter

The result reported by the BOSS experimentfor the Hubble parameter at z = 2.34 is a directevidence for the existence of a non-gravitational coupling between dark energyand dark matter.

H(2.34) = 222 ± 7

H(2.34) = 222 ± 7 result can be explained without interactionand

the EoS we have considered is in no way strange

T. Delubac et al. [BOSS Collaboration], Astron. Astrophys. 574 (2015), A59

E. G. M. Ferreira, J. Quintin, A. A. Costa, E. Abdalla and B. Wang, Phys. Rev. D 95 (2017) no.4, 043520

E. Elizalde, M. Khurshudyan, S. Nojiri, IJMPD (2018)

Interacting Dark Energy models and GP Interacting Dark Energy models and GP

How we can use GP with IDE?

It is very simple task if EoS of DE is given

eventually the interaction term Q will beexpressed as a function of EoS of DE,the Hubble parameter and its higherorder derivatives

Conclusion from this studyConclusion from this studyThe main message from direct numerical integration

1. The model can explain reported value of the Hubble parameter without non-gravitational interaction.

2. The EoS we have considered is in no way strange

The main message from GP

1. we need in this case to involve anon-gravitational interaction betweendark energy and dark matter, to explainthe mentioned value of the Hubbleparameter.

2. However, even if it would seem we doneed to include a non-gravitationalinteraction, this occurs for redshiftsnot covered by recent H(z) data.

we do not have a final answer tothe main question!!!!!

Some resultsSome results

1. The model according 68% C.L. of the reconstruction with 40 sample H(z) data can be accepted.

2. The model according 68% C.L. of the reconstruction with 30 sample H(z) data can be accepted.

3. According to that, either a

or an ω -singularity (Type V) can be generated

S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev. D 71 (2005) 063004M. P. Dabrowski and T. Denkiewicz, Phys. Rev. D 79 (2009) 063521L. Fernandez-Jambrina, Phys. Lett. B 656 (2007) 9

Some other resultsSome other results

The phase space analysis with and gives

ConclusionConclusion

We made an attempt to construct a dark energy model explicitly parametrised by the decelerationparameter. In this way we initiated a fresh direction of research concerning to dynamical dark energymodels.

A detailed study shows that the model (by the direct integration of the field equations) is viable andindicates that we do not need to involve non-gravitational interaction to explain the BOSSexperiment result concerning to Hubble parameter at z = 2.34.

We performed also a model independent analysis using GP and found that in order to address theBOSS experiment issue we need data covering higher redshifts.

On the other hand, we performed the phase space analysis of the models for several forms ofnon-gravitational interaction indicating how the cosmological coincidence problem can besolved.

We have also the classification of the future finite-time singularities for suggested model.

Thank You for Your attention