Deceleration parameter
The deceleration parameter 
  
    
      
        q
      
    
    {\displaystyle q}
   in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by:

  
    
      
        q
         
        
          
            
              
                =
              
              
                
                  d
                  e
                  f
                
              
            
          
        
         
        −
        
          
            
              
                
                  
                    a
                    ¨
                  
                
              
              a
            
            
              
                
                  
                    a
                    ˙
                  
                
              
              
                2
              
            
          
        
      
    
    {\displaystyle q\ {\stackrel {\mathrm {def} }{=}}\ -{\frac {{\ddot {a}}a}{{\dot {a}}^{2}}}}
  where 
  
    
      
        a
      
    
    {\displaystyle a}
   is the scale factor of the universe and the dots indicate derivatives by proper time. The expansion of the universe is said to be "accelerating" if 
  
    
      
        
          
            
              a
              ¨
            
          
        
        >
        0
      
    
    {\displaystyle {\ddot {a}}>0}
   (recent measurements suggest it is), and in this case the deceleration parameter will be negative. The minus sign and name "deceleration parameter" are historical; at the time of definition 
  
    
      
        
          
            
              a
              ¨
            
          
        
      
    
    {\displaystyle {\ddot {a}}}
   was expected to be negative, so a minus sign was inserted in the definition to make 
  
    
      
        q
      
    
    {\displaystyle q}
   positive in that case. Since the evidence for the accelerating universe in the 1998–2003 era, it is now believed that 
  
    
      
        
          
            
              a
              ¨
            
          
        
      
    
    {\displaystyle {\ddot {a}}}
   is positive therefore the present-day value 
  
    
      
        
          q
          
            0
          
        
      
    
    {\displaystyle q_{0}}
   is negative (though 
  
    
      
        q
      
    
    {\displaystyle q}
   was positive in the past before dark energy became dominant).