Relativity and the age of the Universe I put my assistant in a spaceship and accelerate it to near the speed of light.  100 years from now (in my time), my assistant is travelling with speed $0.99c$.  At that time I put up a super sophisticated WMAP-like probe and measure the age of the universe very precisely to be 13.8 billion years (to several decimal places).  My assistant has a similar probe and performs the same measurement.  What age will she calculate for the age of the universe? 
 A: Ignoring the initial acceleration here she would measure it to be exactly the same as from her frame of reference she wasn't moving at all, and it was in fact you that was moving (except for the acceleration at the start).
However for you she would measure the 100 years of time passed to in fact be $$\frac{100}{\sqrt{1-0.99^2}}$$ or $708.88$ years, which whilst being a very large time difference for us as humans, is nothing compared to the age of the universe, and as such it wouldn't affect the age up to a few decimal places in, and uncertainty in the measurement is much larger than this anyway.
A: If shortly after the Big Bang you send your assistant on a trip around a closed universe at a constant speed, she would return $\gamma$ times younger than you. So in her frame the universe would be $\gamma$ times younger than in yours.
The WMAP measurements are made with the CMB dipole removed (speed subtracted), so they would always agree with your clock, but not with hers.
This scenario is not possible in an open universe. The assistant would never return to compare the clocks.
A: The answer is going to be very model-dependent.  
First of all, for the notion of "the age of the Universe" to make any sense,  you need to assume a Universe that's foliated into three dimensional spacelike leaves, with some preferred global time coordinate.  
Next, you seem to be supposing that you and your probe make your measurements "at the same time".  It's not clear whether this means a) at the same time according to you, b) at the same time according to your probe, or c) at the same time according to the preferred global time coordinate. 
So let's see what happens in a very simple model: 

Spacetime is the region in the upper half-plane bounded by $t=-Kx$ and $t=Kx$,  you travel along the worldline $x=0$, until time $T-100$, at which you launch your probe (which gets up to speed immediately).  It travels along the blue worldline to $C$, where it makes its measurement.  You make your own measurement at $B$, which is simulataneous with $C$ according to both you and the preferred global time coordinate.    
You, therefore, declare the age of the Universe to be $T$.
Measured from the origin to $C$, we have $\Delta t=T$ and $\Delta x=99$.  In your probe's coordinates, the time interval  Lorentz transforms to $\Delta t'\approx 7.09(T-98)$  When $T$ is on the order of $13.8$ billion, we can ignore the $98$ and say that your probe will measure the Universe to be about 7 times as old as you do; call it about 98 billion years.  
(On the other hand, if we've all agreed in advance that "the age of the Universe" is to be defined with reference to the preferred global time coordinate, then the probe will of course reject its own measurement and accept yours.)  
