Accelerately Expanding Cosmologies in f(R,Φ,X) Theory

Yıl 2023, Cilt: 27 Sayı: 2, 331 - 336, 25.08.2023

Erkan Eraslan , Melis Ulu Doğru

https://doi.org/10.19113/sdufenbed.1256169

Öz

In this study, beginning and today expansion of universe are viewed in f(R,Φ,X) gravity. Field equations and their solutions of Friedmann-Lemaître-Robertson-Walker cosmologies with perfect fluid are obtained by considering f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) model. Validity of both f(R,Φ,X) gravity and f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) model for non-static space-time geometries is discussed by making use of the obtained matter dynamics results such as pressure and energy density. It is seen that in all obtained solutions by taking into account early and late period expansion, f function is a constant. This indicates that f(R,Φ,X) function is a first-order dependent function of Ricci scalar. When f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) model is considered together, it is understood that the obtained solutions could be reduced to Λ-CDM model for f(R) gravity in limits of Φ→0 and X→0. The fact that the obtained results agree with expected situations supports. So, f(R,Φ,X) theory is a consistent theory of gravity.

Anahtar Kelimeler

f(R Φ X) Gravity, Perfect Fluid, Friedmann- Lemaître-Robertson-Walker Space-Time

Destekleyen Kurum

Çanakkale Onsekiz Mart University Scientific Research Projects Coordination Unit

Proje Numarası

4201

Teşekkür

This study is a part of the master's thesis titled with " f(R,Φ,X) Theory" prepared by Erkan Eraslan. This study was supported by Çanakkale Onsekiz Mart University Scientific Research Projects Coordination Unit. Project Number: 4201.

f(R,Φ,X) Teori'de İvmeli Genişleyen Kozmolojiler

Öz

Bu çalışmada, evrenin başlangıç ve günümüz genişlemesi, f(R,Φ,X) gravite çerçevesinde gözden geçirilmiştir. İdeal akışkanlı Friedmann-Lemaître-Robertson-Walker uzay-zamanı için alan denklemleri ve çözümleri f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) modeli dikkate alınarak elde edilmiştir. Statik olmayan uzay-zaman geometrileri için f(R,Φ,X) gravite ve f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) modelinin geçerliliği basınç ve enerji yoğunluğu gibi elde edilen madde dinamikleri kullanılarak tartışılmıştır. Elde edilen sonuçlardan erken ve geç dönem genişlemeleri için f fonksiyonunun sabit değer aldığı görülmüştür. Bu durum f(R,Φ,X) fonksiyonunun Ricci skalerine birinci dereceden bağlı bir fonksiyon olduğunu göstermektedir. f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) modeli ile birlikte düşünüldüğünde Φ→0 ve X→0 limitinde elde edilen çözümlerin f(R) gravitenin Λ-CDM modeline indirgeneceği anlaşılmaktadır. Öyleki elde edilen çözümlerin beklenen durum ile uyuşum içinde olması teorinin tutarlı bir gravitasyon teorisi olduğunu desteklemektedir.

Anahtar Kelimeler

f(R Φ X) Gravite, İdeal akışkan, Friedmann- Lemaître-Robertson-Walker Uzay-Zamanı

Proje Numarası

4201

Kaynakça

• [1] B Riess, A. G., Filippenko, A. V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P. M., ... & Tonry, J. (1998). Observational evidence from supernovae for an accelerating universe and a cosmological constant. The Astronomical Journal, 116(3), 1009.
• [2] Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R. A., Nugent, P., Castro, P. G., ... & Supernova Cosmology Project. (1999). Measurements of Ω and Λ from 42 high-redshift supernovae. The Astrophysical Journal, 517(2), 565.
• [3] Astier, P., Guy, J., Regnault, N., Pain, R., Aubourg, E., Balam, D., & Walton, N. (2006). The Supernova Legacy Survey: measurement of, and w from the first year data set. Astronomy & Astrophysics, 447(1), 31-48.
• [4] Copeland, E. J., Sami, M., & Tsujikawa, S. (2006). Dynamics of dark energy. International Journal of Modern Physics D, 15(11), 1753-1935.
• [5] Brans, C., & Dicke, R. H. (1961). Mach's principle and a relativistic theory of gravitation. Physical review, 124(3), 925.
• [6] Buchdahl, H. A. (1970). Non-linear Lagrangians and cosmological theory. Monthly Notices of the Royal Astronomical Society, 150(1), 1-8.
• [7] Harko, T., Lobo, F. S., Nojiri, S. I., & Odintsov, S. D. (2011). f (R, T) gravity. Physical Review D, 84(2), 024020.
• [8] Stabile, A., & Capozziello, S. (2013). Galaxy rotation curves in f (R, ϕ) gravity. Physical Review D, 87(6), 064002.
• [9] Armendáriz-Picón, C., Mukhanov, V. F., & Steinhardt, P. J. (2001). Essentials of k-essence. Phys. Rev. D 63, 103510.
• [10] Hwang, J. C., & Noh, H. (2002). Cosmological perturbations in a generalized gravity including tachyonic condensation. Physical Review D, 66(8), 084009.
• [11] Tsujikawa, S. (2007). Matter density perturbations and effective gravitational constant in modified gravity models of dark energy. Physical Review D, 76(2), 023514. [12] Bahamonde, S., Böhmer, C. G., Lobo, F. S., & Sáez-Gómez, D. (2015). Generalized f (R, ϕ, X) gravity and the late-time cosmic acceleration. Universe, 1(2), 186-198.
• [13] Nicolis, A., Rattazzi, R., & Trincherini, E. (2009). Galileon as a local modification of gravity. Physical Review D, 79(6), 064036.
• [14] Schimd, C., Uzan, J. P., & Riazuelo, A. (2005). Weak lensing in scalar-tensor theories of gravity. Physical Review D, 71(8), 083512.
• [15] Ishak, M., Upadhye, A., & Spergel, D. N. (2006). Probing cosmic acceleration beyond the equation of state: Distinguishing between dark energy and modified gravity models. Physical Review D, 74(4), 043513.
• [16] Huterer, D., & Linder, E. V. (2007). Separating dark physics from physical darkness: Minimalist modified gravity versus dark energy. Physical Review D, 75(2), 023519.
• [17] Hu, W., & Sawicki, I. (2007). Models of f (R) cosmic acceleration that evade solar system tests. Physical Review D, 76(6), 064004.
• [18] Starobinsky, A. A. (2007). Disappearing cosmological constant in f (R) gravity. JETP letters, 86(3), 157-163.
• [19] Tsujikawa, S. (2008). Observational signatures of f (R) dark energy models that satisfy cosmological and local gravity constraints. Physical Review D, 77(2), 023507.
• [20] Boisseau, B., Esposito-Farese, G., Polarski, D., & Starobinsky, A. A. (2000). Reconstruction of a scalar-tensor theory of gravity in an accelerating universe. Physical Review Letters, 85(11), 2236.
• [21] Riazuelo, A., & Uzan, J. P. (2002). Cosmological observations in scalar-tensor quintessence. Physical Review D, 66(2), 023525.
• [22] Malik, A., Nafees, A., Ali, A., & Butt, M. N. (2022). A study of cylindrically symmetric solutions in $$ f (R,\phi, X) $$ f (R, ϕ, X) theory of gravity. The European Physical Journal C, 82(2), 1-22.