Eur. Phys. J. C (2009) 62: 579–586 DOI 10.1140/epjc/s10052-009-1056-5 Regular Article - Theoretical Physics Relaxing the cosmological constraints on unparticle dark component Hao Weia Department of Physics, Beijing Institute of Technology, Beijing 100081, China Received: 7 February 2009 / Revised: 22 April 2009 / Published online: 3 June 2009 © Springer-Verlag / Società Italiana di Fisica 2009 Abstract Unparticle physics has been an active field since where P is the 4-momentum; Adu is the normalization fac- the seminal work of Georgi. Recently, many constraints on tor; du is the scaling dimension. When du = 1, (1) reduces to unparticles from various observations have been considered the familiar one of a massless particle. The scaling dimen- in the literature. In particular, the cosmological constraints sion du is constrained by the unitarity of the conformal alge- on the unparticle dark component put it in a serious situa- bra and the requirement to avoid the singular behavior [1, 4]. tion. In this work, we try to find a way out of this serious The theoretical bounds are 1 ≤ du ≤ 2 (for bosonic unparti- situation, by including the possible interaction between dark cles) or 3/2 ≤ du ≤ 5/2 (for fermionic unparticles) [4]. Typ- energy and the unparticle dark component. ically, values 1 ≤ du ≤ 2 have been extensively considered in the literature. PACS 98.80.Es · 14.80.-j · 95.36.+x · 98.80.-k The pressure and energy density of thermal unparticles have been derived in [23]. They are − T 2(du 1) C(d ) 1 Introduction p = g T 4 u , u s 2 (2) Λu 4π − Recently, the so-called unparticle physics has been an active T 2(du 1) C(d ) ρ = ( d + )g T 4 u , u 2 u 1 s 2 (3) field since the seminal work of Georgi [1, 2]. It was based Λu 4π on the hypothesis that there could be an exact scale invariant C = + + hidden sector resisted at a high energy scale. A prototype where (du) B(3/2,du)Γ (2du 2)ζ(2du 2), while B, model of such a sector is given by the Banks–Zaks theory Γ , ζ are the Beta, Gamma and Zeta functions, respec- which flows to an infrared fixed point at a lower energy scale tively. These are the results for the bosonic unparticles. The pressure and energy density of fermionic unparticles can Λu through dimensional transmutation [3]. Recently, there − + C [ − (2du 1)]C has been a flood of papers on the unparticle phenomenol- be obtained by replacing (du) by 1 2 (du). ogy. We refer to e.g. [3, 4] for some brief reviews. In fact, Therefore, the equation-of-state parameter (EoS) of both the soon after the seminal work of Georgi [1, 2], some authors bosonic and fermionic unparticles is given by [23] considered the constraints on unparticles from various ob- ≡ pu = 1 servations, such as collider experiments [5–7], the new long wu . (4) ρu 2du + 1 range force experiments [8–11], the solar and reactor neu- = = trinos data [12, 13], as well as the observations from astro- When du 1, we have wu 1/3, which is the same as radi- →∞ → physics and cosmology [11, 14–22, 47]. These observations ation. When du , we find wu 0, which approaches put fairly stringent constraints on the unparticle. the EoS of pressureless matter. In the intermediate case, the The unparticle does not have a definite mass and instead EoS of unparticles is different from the one of radiation or has a continuous spectral density as a consequence of scale cold dark matter and generically lies in between. Since the invariance [1, 2](seealsoe.g.[22, 23, 48]), unparticle interacts weakly with standard model particles, it is “dark” in this sense. Some authors regard the unparticle as − 2 = 0 2 2 du 2 a candidate of dark matter [24, 25](seealso[22, 23]). Not- ρ P Adu θ P θ P P , (1) ing that the EoS of unparticles (wu > 0) is different from the one of cold dark matter (wm = 0), we instead call it “dark a e-mail: [email protected] component” to avoid confusion. 580 Eur. Phys. J. C (2009) 62: 579–586 In [22], the cosmological constraints on the unparticle So, the total energy conservation equation ρ˙tot + 3Hρtot × dark component have been considered, by using the type Ia (1 + wtot) = 0 is preserved. H ≡˙a/a is the Hubble para- supernovae (SNIa), the shift parameter of the cosmic mi- meter; a = (1 + z)−1 is the scale factor of the universe (we crowave background (CMB), and the baryon acoustic os- set a0 = 1); the subscript “0” indicates the present value of cillation (BAO). The authors of [22] found that du > 60 the corresponding quantity; z is the redshift; a dot denotes at 95% confidence level (C.L.) for the ΛUDM model in the derivative with respect to cosmic time t. The interac- which the unparticle is the sole dark matter. As mentioned tion forms extensively considered in the literature (see for above, however, the theoretical bounds on unparticles are instance [26–34, 49] and references therein) are Q ∝ Hρm, ≤ ≤ ≤ ≤ ˙ 2 1 du 2 (for bosonic unparticles) or 3/2 du 5/2 (for Hρde, Hρtot, κρmφ (where κ ≡ 8πG), and so on. In this fermionic unparticles) [4]. The situation is serious. Even for work, for simplicity, we consider the interaction term the ΛUCDM model in which the unparticle dark component co-exists with cold dark matter, they found that the unparti- Q = 3αHρu, (8) cle dark component can at most make up a few percent of the total cosmic energy density if du < 10; so that it cannot where α is a constant. So (6) becomes ρ˙u + 3Hρu × + eff = eff ≡ − be a major component [22]. In fact, it is easy to understand (1 wu ) 0, where wu wu α. It is easy to find that these results. Since the unparticle dark component scales as −3(1+wu) −3 −3(1+weff) a whereas cold dark matter scales as a (here a is ρu = ρu0a u . (9) the scale factor of the universe), for wu > 0, the energy den- −3 sity of the unparticle dark component decreases faster than On the other hand, from (7), we have ρm = ρm0 a .For the one of cold dark matter. So it is not surprising that the convenience, we introduce the fractional energy density 2 energy density of the unparticle dark component cannot be Ωi ≡ (8πGρi)/(3H ), where i = de, u and m. comparable with cold dark matter at the present epoch. To In the following sections, similar to [22], we consider the make a considerable contribution to the total cosmic energy cosmological constraints on the unparticle dark component density, du should be very large to make wu 0 so that the which interacts with dark energy, by using the observations unparticle dark component could mimic cold dark matter. of SNIa, the shift parameter R of CMB, and the distance pa- In this work, we try to find a way out of the serious situa- rameter A from BAO. In Sect. 2, we present the cosmolog- tion mentioned above. Our physical motivation is very sim- ical data and the methodology used to constrain the mod- ple. If dark energy, the major component of the universe, can els. In Sects. 3 and 4, we consider the observational con- decay into unparticles, the energy density of the unparticle straints on the interacting ΛUCDM model and the interact- dark component should decrease more slowly. Since both ing XUCDM model, respectively. As expected, we find that dark energy and unparticle are unseen, the interaction be- the cosmological constraints on the unparticle dark compo- tween them is not prevented. If the dilution rates of unpar- nent can be significantly relaxed, thanks to the possible in- ticle dark component and cold dark matter are comparable, teraction between dark energy and unparticle dark compo- it is possible to have a considerable energy density of the nent. The tension between theoretical bounds and cosmolog- unparticle dark component at the present epoch, without re- ical constraints could be removed. Finally, some concluding quiring d to be very large. In fact, this is similar to the key u remarks are given in Sect. 5. point of the interacting dark energy models which are exten- sively considered in the literature to alleviate the cosmologi- cal coincidence problem (see e.g. [26–34, 49] and references therein). 2 Cosmological data Here, we consider a flat universe which contains dark en- ergy, the unparticle dark component and pressureless mat- In this work, we perform a χ2 analysis to obtain the con- ter (including cold dark matter and baryons). We assume straints on the model parameters. The data points of the 307 that dark energy and unparticle dark component exchange Union SNIa compiled in [35] are given in terms of the dis- energy according to (see e.g. [26–34, 49] and references tance modulus μobs(zi). On the other hand, the theoretical therein) distance modulus is defined as ρ˙ + 3Hρ (1 + w ) =−Q, (5) ≡ + de de de μth(zi) 5log10 DL(zi) μ0, (10) ρ˙ + 3Hρ (1 + w ) = Q, (6) u u u ≡ − where μ0 42.38 5log10 h and h is the Hubble constant whereas pressureless matter (including cold dark matter and H0 in units of 100 km/s/Mpc, whereas baryons) evolves independently, i.e., z dz˜ DL(z) = (1 + z) , (11) ρ˙m + 3Hρm = 0. (7) 0 E(z˜; p) Eur. Phys. J. C (2009) 62: 579–586 581 in which E ≡ H/H0; p denotes the model parameters.