\begin{document}$ f(\bar{R}, L(X))- $\end{document}gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where \begin{document}$ \bar{R} $\end{document} is the familiar Ricci scalar, \begin{document}$ L(X) $\end{document} is the DBI type non-canonical Lagrangian with \begin{document}$ X={1\over 2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi $\end{document}, and ϕ is the K-essence scalar field. The emergent gravity metric (\begin{document}$ {\bar{G}}_{\mu\nu} $\end{document}) and the well known gravitational metric (\begin{document}$ g_{\mu\nu} $\end{document}) are not conformally equivalent. We have constructed a modified field equation using the metric formalism in \begin{document}$ f(\bar{R}, L(X)) $\end{document}-gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choice of \begin{document}$ f(\bar{R}, L(X)) $\end{document}, which is of Starobinsky-type, using the power law expansion method. The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as \begin{document}$\dot\phi^{2}=8/9=0.888 < 1$\end{document}, which indicates that the present universe is dark-energy dominated. Graphical plots for the energy density (ρ), pressure (p), and equation of state parameter (\begin{document}$ {\omega} $\end{document}) with respect to (w.r.t.) time (t) based on parametric values are interestingly consistent with the dark energy domination theory, and hence the accelerating features. We also highlight the corresponding energy conditions and constraints of the \begin{document}$ f(\bar{R}, L(X)) $\end{document} theory with a basic example."> <inline-formula><tex-math id="M1">\begin{document}${ \boldsymbol f(\bar{\boldsymbol R}, \boldsymbol L(\boldsymbol X))} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/f852f10a-9d6f-4686-9da6-773f65910953/CPC-2022-0382_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/f852f10a-9d6f-4686-9da6-773f65910953/CPC-2022-0382_M1.png"/></alternatives></inline-formula>-gravity in the context of dark energy with power law expansion and energy conditions -
  • [1]

    H. Weyl, Ann. Phys.59, 101 (1919)

  • [2]

    A.S. Eddington,The mathematical theory of relativity, Cambridge University Press, Cambridge (1923).

  • [3]

    R. Utiyama, B.S. DeWitt, J. Math. Phys.3, 608 (1962)

  • [4]

    N.D. Birrell, P.C.W. Davies,Quantum fields in curved spacetime, Cambridge University Press, Cambridge (1982).

  • [5]

    A.A. Starobinsky, Phys. Lett. B91, 9 (1980)

  • [6]

    T.P. Sotiriou and V. Faraoni, Rev. of Mod. Phys.82, 451 (2010)

  • [7]

    A. De Felice and S. Tsujikawa, Living Rev. Relativ.13, 3 (2010)

  • [8]

    P. K. S. Dunsbyet al., Phys. Rev. D82, 023519 (2010)

  • [9]

    A. Mukherjee and N. Banerjee, Astrophys. Space Sci.352, 893 (2014)

  • [10]

    K. Atazadehet al., Int. J. Mod. Phys. D18, 1101 (2009)

  • [11]

    J. Santoset al., Phys. Rev. D76, 083513 (2007)

  • [12]

    S. Capozzielloet al., Phys. Lett. B781, 99 (2018)

  • [13]

    J. Wanget al., Phys. Lett. B689, 133 (2010)

  • [14]

    S. E. Perez Bergliaffa, Phys. Lett. B642, 311 (2006)

  • [15]

    F. D. Albaretiet al., JCAP03, 012 (2014)

  • [16]

    F. D. Albaretiet al., JCAP07, 009 (2013)

  • [17]

    K. D. Kroriet al., Ind. J. Phys.82(5), 531 (2008)

  • [18]

    T. Harko and F. S. N. Lobo, Eur. Phys. J. C70, 373 (2010)

  • [19]

    J. Wang and K. Liao, Class. Quantum Gravit.29, 215016 (2012)

  • [20]

    N. Goheer, R. Goswami, P. K. S. Dunsbyet al., Phys. Rev. D79, 121301(R) (2009)

  • [21]

    N. Goheer, J. Larena, and P. K. S. Dunsby, Phys. Rev. D80, 061301 (2009)

  • [22]

    C. P. Singh and V. Singh, Int. J. Theor. Phys.51, 1889 (2012)

  • [23]

    T. Harkoet al., Phys. Rev. D84, 024020 (2011)

  • [24]

    N. Hulke, G. P. Singh, B. K. Bishiet al., New Astronomy77, 101357 (2020)

  • [25]

    A. Pradhan, A. Dixit, and G. Varshney, Int. J. Mod. Phys. A37, 2250121 (2022)

  • [26]

    V. K. Bhardwaj and A. Pradhan, New Astron.91, 101675 (2022)

  • [27]

    A. Pradhan, D. C. Maurya, G. K. Goswamiet al.Modeling Transit Dark Energy in \begin{document}$f(R, L_m)$\end{document} -gravity, arXiv:2209.14269

  • [28]

    C. Armendariz-Piconet al., Phys. Rev. D63, 103510 (2001)

  • [29]

    C. Armendariz-Piconet al., Phys. Rev. Lett.85, 4438 (2000)

  • [30]

    M. Visser, C. Barcelo, and S. Liberati, Gen. Relativ. Gravit.34, 1719 (2002)

  • [31]

    E. Babichev, V. Mukhanov, and A. Vikman, JHEP0609, 061 (2006)

  • [32]

    E. Babichev, V. Mukhanov, and A. Vikman, JHEP02, -101 (2008)

  • [33]

    A. Vikman,K-essence: Cosmology, causality and Emergent Geometry, Dissertation an der Fakultat fur Physik, Arnold Sommerfeld Center for Theoretical Physics, der Ludwig-Maximilians-Universitat Munchen, Munchen, den 29.08.2007.

  • [34]

    E. Babichev, V. Mukhanov, A. Vikman,Looking beyond the Horizon, WSPC-Proceedings (October 23, 2008).

  • [35]

    R. J. Scherrer, Phys. Rev. Lett.93, 011301 (2004)

  • [36]

    L. P. Chimento, Phys. Rev. D69, 123517 (2004)

  • [37]

    M. Born and L. Infeld, Proc. Roy. Soc. Lond A144, 425 (1934)

  • [38]

    W. Heisenberg, Zeit. Phys.113, 61 (1939)

  • [39]

    P. A. M. Dirac, Proc. R. Soc. Lond. A268, 57 (1962)

  • [40]

    D. Gangopadhyay and G. Manna, Eur. Phys. Lett.100, 49001 (2012)

  • [41]

    G. Manna and D. Gangopadhyay, Eur. Phys. J. C74, 2811 (2014)

  • [42]

    G. Manna, B. Majumder, Eur. Phys. J. C79, 553 (2019)

  • [43]

    S. Mukohyamaet al., Phys. Rev. D94, 023514 (2016)

  • [44]

    S. Nojiri et. al., Nuc. Phys. B94, 11 (2019)

  • [45]

    S. D. Odintsov et. al., Phys. Dark Univ.29, 100563 (2020)

  • [46]

    V. K. Oikonomou and N. Chatzarakis, Nuc. Phys. B956, 115023 (2020)

  • [47]

    N. Bahcallet al., Science284, 1481 (1999)

  • [48]

    J. U. Kanget al., Phys. Rev. D.76, 083511 (2007)

  • [49]

    R. R. Caldwellet al., Phys. Rev. Lett.80, 1582 (1998)

  • [50]

    J. Friemanet al., Phys. Rev. Lett.75, 2077 (1995)

  • [51]

    P. J. E. Peebles and B. Ratra, Astrophys. J. Lett.325, L17 (1988)

  • [52]

    B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988)

  • [53]

    I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999)

  • [54]

    P. J. Steinhardt, L. Wang, and I. Zlatev, Phys. Rev. D59, 123504 (1999)

  • [55]

    I. Zlatev, Limin Wang, and P. J. Steinhardt, Phys. Rev. Lett.82, 896 (1999)

  • [56]

    J.K. Ericksonet al., Phys. Rev. Lett.88, 121301 (2002)

  • [57]

    S. DeDeo, R. R. Caldwell, and P. J. Steinhardt, Phys. Rev. D67, 103509 (2003)

  • [58]

    R. Bean and O. Dore, Phys. Rev. D69, 083503 (2004)

  • [59]

    C. Bonvin et. al., Phys. Rev. Lett.97, 081303 (2006)

  • [60]

    R. Yanget al., Astrophys. Space Sci.356, 399 (2014)

  • [61]

    I. Sawickiet al., Phys. Rev. D88, 083520 (2013)

  • [62]

    M. Kunzet al., Phys. Rev. D92, 063006 (2015)

  • [63]

    A.D. Linde, Phys. Lett. B108, 389 (1982)

  • [64]

    A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett.48, 1220 (1982)

  • [65]

    G. Dvali and S.-H. Henry Tye, Phys. Lett. B450, 72 (1999)

  • [66]

    S. Kachruet al., JCAP0310, 013 (2003)

  • [67]

    M. Alishahiha, E. Silverstein, and D. Tong, Phys. Rev. D70, 123505 (2004)

  • [68]

    E. Silverstein and D. Tong, Phys. Rev. D70, 103505 (2004)

  • [69]

    X. Chen, Phys. Rev. D71, 063506 (2005)

  • [70]

    S. Weinberg, Phys. Rev. D77, 123541 (2008)

  • [71]

    X. Chenet al., JCAP0701, 002 (2007)

  • [72]

    Pandaet al., " \begin{document}$f(\bar{R}, T)-$\end{document} gravity in the context of dark energy",https://doi.org/10.48550/arXiv.2206.14808(2022)

  • [73]

    S. Carroll,Spacetime and Geometry: An Introduction to General Relativity, Addison Wesley, New York (2004).

  • [74]

    D. Gangopadhyay, G. Manna,Cosmology in presence of dark energy in an emergent gravity scenario, arXiv:1502.06255

  • [75]

    R.M. Wald,General Relativity, Univ. Chicago Press (1984).

  • [76]

    C. Misner, K.S. Thorne, J. Wheeler,Gravitation, W.H. Freeman and Company (1970).

  • [77]

    T. Koivisto, Class. Quantum Gravit.23, 4289 (2006)

  • [78]

    T. Harko, Phys. Lett. B669, 376 (2008)

  • [79]

    A. Kehagiaset al., Phys. Rev. D89, 043527 (2013)

  • [80]

    P. H. R. S. Moraeset al., Adv. Astron., 8574798 (2019)

  • [81]

    A. Tripathiet al., JCAP06, 12 (2017)

  • [82]

    E. R. Harrison, Nature (London)260, 591 (1976)

  • [83]

    P. Landsberg, Nature (London)263, 217 (1976)

  • [84]

    M. Visser, Class. Quantum Gravit.21, 2603 (2004)

  • [85]

    M. Visser, Gen. Relativ. Gravit.37, 1541 (2005)

  • [86]

    P. R. Adeet al., Astron. Astrophys.594, A13 (2016)

  • [87]

    N. Aghanimet al., Astron. Astrophys.641, A6 (2020)

  • [88]

    J. T. Nielsen, A Guffanti, and S. Sarkar, Sci. Rep.6, 35596 (2016)

  • [89]

    A. Raychaudhuri, Phys. Rev.98, 1123 (1955)

  • [90]

    A. Raychaudhuri, Z. Astrophysik.43, 161 (1957)

  • [91]

    A. Raychaudhuri, Phys. Rev.106, 172 (1957)

  • [92]

    M. Blau,Lecture Notes on General Relativity,http://www.blau.itp.unibe.ch/GRLecturenotes.html(2020).

  • [93]

    I. Bhattacharyya and S. Ray, Int. J. Mod. Phys. D30, 2150092 (2021)

  • [94]

    I. Bhattacharyya and S. Ray, Eur. Phys. J. C82, 953 (2022)

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